Results of Bessel Functions I: Difference between revisions

Revision as of 19:51, 15 October 2020

This is the first half of the chapter Bessel Functions. It from Section 10.2 to 10.32. For Section 10.33 to 10.73 go to Bessel Functions II.

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.2.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}+(z^{2}-\nu^{2})w = 0}	`(z)^(2)* diff(w, [z$(2)])+ zdiff(w, z)+((z)^(2)- (nu)^(2)) w = 0`	`(z)^(2)* D[w, {z, 2}]+ zD[w, z]+((z)^(2)- \[Nu]^(2)) w == 0`	Failure	Failure	Failed [217 / 300] `217/300]: [[-.8660254040e-9-2.000000001I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}` `-.8660254040e-9-2.000000001I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)}`	Failed [240 / 300] `{Complex[1.1102230246251565^-16, 2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}` `Complex[1.1102230246251565^-16, 2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}`
10.2.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}}	`BesselJ(nu, z) = ((1)/(2)z)^(nu) sum((- 1)^(k)(((1)/(4)(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity)`	`BesselJ[\[Nu], z] == (Divide[1,2]z)^\[Nu] Sum[(- 1)^(k)Divide[(Divide[1,4](z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 70]
10.2.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{\BesselJ{\nu}@{z}\cos@{\nu\pi}-\BesselJ{-\nu}@{z}}{\sin@{\nu\pi}}}	`BesselY(nu, z) = (BesselJ(nu, z)cos(nuPi)- BesselJ(- nu, z))/(sin(nu*Pi))`	`BesselY[\[Nu], z] == Divide[BesselJ[\[Nu], z]Cos[\[Nu]Pi]- BesselJ[- \[Nu], z],Sin[\[Nu]*Pi]]`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.4#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-n}@{z} = (-1)^{n}\BesselJ{n}@{z}}	`BesselJ(- n, z) = (- 1)^(n)* BesselJ(n, z)`	`BesselJ[- n, z] == (- 1)^(n)* BesselJ[n, z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.4#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{-n}@{z} = (-1)^{n}\BesselY{n}@{z}}	`BesselY(- n, z) = (- 1)^(n)* BesselY(n, z)`	`BesselY[- n, z] == (- 1)^(n)* BesselY[n, z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.4#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{-n}@{z} = (-1)^{n}\HankelH{1}{n}@{z}}	`HankelH1(- n, z) = (- 1)^(n)* HankelH1(n, z)`	`HankelH1[- n, z] == (- 1)^(n)* HankelH1[n, z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.4#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{-n}@{z} = (-1)^{n}\HankelH{2}{n}@{z}}	`HankelH2(- n, z) = (- 1)^(n)* HankelH2(n, z)`	`HankelH2[- n, z] == (- 1)^(n)* HankelH2[n, z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.4#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \BesselJ{\nu}@{z}+i\BesselY{\nu}@{z}}	`HankelH1(nu, z) = BesselJ(nu, z)+ I*BesselY(nu, z)`	`HankelH1[\[Nu], z] == BesselJ[\[Nu], z]+ I*BesselY[\[Nu], z]`	Successful	Successful	-	Successful [Tested: 70]
10.4#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \BesselJ{\nu}@{z}-i\BesselY{\nu}@{z}}	`HankelH2(nu, z) = BesselJ(nu, z)- I*BesselY(nu, z)`	`HankelH2[\[Nu], z] == BesselJ[\[Nu], z]- I*BesselY[\[Nu], z]`	Successful	Successful	-	Successful [Tested: 70]
10.4#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2}\left(\HankelH{1}{\nu}@{z}+\HankelH{2}{\nu}@{z}\right)}	`BesselJ(nu, z) = (1)/(2)*(HankelH1(nu, z)+ HankelH2(nu, z))`	`BesselJ[\[Nu], z] == Divide[1,2]*(HankelH1[\[Nu], z]+ HankelH2[\[Nu], z])`	Successful	Successful	-	Successful [Tested: 70]
10.4#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{1}{2i}\left(\HankelH{1}{\nu}@{z}-\HankelH{2}{\nu}@{z}\right)}	`BesselY(nu, z) = (1)/(2I)(HankelH1(nu, z)- HankelH2(nu, z))`	`BesselY[\[Nu], z] == Divide[1,2I](HankelH1[\[Nu], z]- HankelH2[\[Nu], z])`	Successful	Successful	-	Successful [Tested: 70]
10.4.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-\BesselY{\nu}@{z}\cos@{\nu\pi}\right)}	`BesselJ(nu, z) = csc(nuPi)(BesselY(- nu, z)- BesselY(nu, z)cos(nuPi))`	`BesselJ[\[Nu], z] == Csc[\[Nu]Pi](BesselY[- \[Nu], z]- BesselY[\[Nu], z]Cos[\[Nu]Pi])`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.4#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{-\nu}@{z} = e^{\nu\pi i}\HankelH{1}{\nu}@{z}}	`HankelH1(- nu, z) = exp(nuPiI)*HankelH1(nu, z)`	`HankelH1[- \[Nu], z] == Exp[\[Nu]PiI]*HankelH1[\[Nu], z]`	Successful	Failure	-	Successful [Tested: 70]
10.4#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{-\nu}@{z} = e^{-\nu\pi i}\HankelH{2}{\nu}@{z}}	`HankelH2(- nu, z) = exp(- nuPiI)*HankelH2(nu, z)`	`HankelH2[- \[Nu], z] == Exp[- \[Nu]PiI]*HankelH2[\[Nu], z]`	Successful	Failure	-	Successful [Tested: 70]
10.4.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = i\csc@{\nu\pi}\left(e^{-\nu\pi i}\BesselJ{\nu}@{z}-\BesselJ{-\nu}@{z}\right)}	`HankelH1(nu, z) = Icsc(nuPi)(exp(- nuPiI)BesselJ(nu, z)- BesselJ(- nu, z))`	`HankelH1[\[Nu], z] == ICsc[\[Nu]Pi](Exp[- \[Nu]PiI]BesselJ[\[Nu], z]- BesselJ[- \[Nu], z])`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.4.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\csc@{\nu\pi}\left(e^{-\nu\pi i}\BesselJ{\nu}@{z}-\BesselJ{-\nu}@{z}\right) = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-e^{-\nu\pi i}\BesselY{\nu}@{z}\right)}	`Icsc(nuPi)(exp(- nuPiI)BesselJ(nu, z)- BesselJ(- nu, z)) = csc(nuPi)(BesselY(- nu, z)- exp(- nuPiI)*BesselY(nu, z))`	`ICsc[\[Nu]Pi](Exp[- \[Nu]PiI]BesselJ[\[Nu], z]- BesselJ[- \[Nu], z]) == Csc[\[Nu]Pi](BesselY[- \[Nu], z]- Exp[- \[Nu]PiI]*BesselY[\[Nu], z])`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.4.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = i\csc@{\nu\pi}\left(\BesselJ{-\nu}@{z}-e^{\nu\pi i}\BesselJ{\nu}@{z}\right)}	`HankelH2(nu, z) = Icsc(nuPi)(BesselJ(- nu, z)- exp(nuPiI)BesselJ(nu, z))`	`HankelH2[\[Nu], z] == ICsc[\[Nu]Pi](BesselJ[- \[Nu], z]- Exp[\[Nu]PiI]BesselJ[\[Nu], z])`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.4.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\csc@{\nu\pi}\left(\BesselJ{-\nu}@{z}-e^{\nu\pi i}\BesselJ{\nu}@{z}\right) = \csc@{\nu\pi}\left(\BesselY{-\nu}@{z}-e^{\nu\pi i}\BesselY{\nu}@{z}\right)}	`Icsc(nuPi)(BesselJ(- nu, z)- exp(nuPiI)BesselJ(nu, z)) = csc(nuPi)(BesselY(- nu, z)- exp(nuPiI)*BesselY(nu, z))`	`ICsc[\[Nu]Pi](BesselJ[- \[Nu], z]- Exp[\[Nu]PiI]BesselJ[\[Nu], z]) == Csc[\[Nu]Pi](BesselY[- \[Nu], z]- Exp[\[Nu]PiI]*BesselY[\[Nu], z])`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.5.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\BesselJ{-\nu}@{z}} = \BesselJ{\nu+1}@{z}\BesselJ{-\nu}@{z}+\BesselJ{\nu}@{z}\BesselJ{-\nu-1}@{z}}	`(BesselJ(nu, z))diff(BesselJ(- nu, z), z)-diff(BesselJ(nu, z), z)(BesselJ(- nu, z)) = BesselJ(nu + 1, z)BesselJ(- nu, z)+ BesselJ(nu, z)BesselJ(- nu - 1, z)`	`Wronskian[{BesselJ[\[Nu], z], BesselJ[- \[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]BesselJ[- \[Nu]- 1, z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.5.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\BesselJ{-\nu}@{z}+\BesselJ{\nu}@{z}\BesselJ{-\nu-1}@{z} = -2\sin@{\nu\pi}/(\pi z)}	`BesselJ(nu + 1, z)BesselJ(- nu, z)+ BesselJ(nu, z)BesselJ(- nu - 1, z) = - 2sin(nuPi)/(Pi*z)`	`BesselJ[\[Nu]+ 1, z]BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]BesselJ[- \[Nu]- 1, z] == - 2Sin[\[Nu]Pi]/(Pi*z)`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.5.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\BesselY{\nu}@{z}} = \BesselJ{\nu+1}@{z}\BesselY{\nu}@{z}-\BesselJ{\nu}@{z}\BesselY{\nu+1}@{z}}	`(BesselJ(nu, z))diff(BesselY(nu, z), z)-diff(BesselJ(nu, z), z)(BesselY(nu, z)) = BesselJ(nu + 1, z)BesselY(nu, z)- BesselJ(nu, z)BesselY(nu + 1, z)`	`Wronskian[{BesselJ[\[Nu], z], BesselY[\[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]BesselY[\[Nu], z]- BesselJ[\[Nu], z]BesselY[\[Nu]+ 1, z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.5.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\BesselY{\nu}@{z}-\BesselJ{\nu}@{z}\BesselY{\nu+1}@{z} = 2/(\pi z)}	`BesselJ(nu + 1, z)BesselY(nu, z)- BesselJ(nu, z)BesselY(nu + 1, z) = 2/(Pi*z)`	`BesselJ[\[Nu]+ 1, z]BesselY[\[Nu], z]- BesselJ[\[Nu], z]BesselY[\[Nu]+ 1, z] == 2/(Pi*z)`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.5.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\HankelH{1}{\nu}@{z}} = \BesselJ{\nu+1}@{z}\HankelH{1}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{1}{\nu+1}@{z}}	`(BesselJ(nu, z))diff(HankelH1(nu, z), z)-diff(BesselJ(nu, z), z)(HankelH1(nu, z)) = BesselJ(nu + 1, z)HankelH1(nu, z)- BesselJ(nu, z)HankelH1(nu + 1, z)`	`Wronskian[{BesselJ[\[Nu], z], HankelH1[\[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]HankelH1[\[Nu], z]- BesselJ[\[Nu], z]HankelH1[\[Nu]+ 1, z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.5.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\HankelH{1}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{1}{\nu+1}@{z} = 2i/(\pi z)}	`BesselJ(nu + 1, z)HankelH1(nu, z)- BesselJ(nu, z)HankelH1(nu + 1, z) = 2I/(Piz)`	`BesselJ[\[Nu]+ 1, z]HankelH1[\[Nu], z]- BesselJ[\[Nu], z]HankelH1[\[Nu]+ 1, z] == 2I/(Piz)`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.5.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJ{\nu}@{z},\HankelH{2}{\nu}@{z}} = \BesselJ{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{2}{\nu+1}@{z}}	`(BesselJ(nu, z))diff(HankelH2(nu, z), z)-diff(BesselJ(nu, z), z)(HankelH2(nu, z)) = BesselJ(nu + 1, z)HankelH2(nu, z)- BesselJ(nu, z)HankelH2(nu + 1, z)`	`Wronskian[{BesselJ[\[Nu], z], HankelH2[\[Nu], z]}, z] == BesselJ[\[Nu]+ 1, z]HankelH2[\[Nu], z]- BesselJ[\[Nu], z]HankelH2[\[Nu]+ 1, z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.5.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\BesselJ{\nu}@{z}\HankelH{2}{\nu+1}@{z} = -2i/(\pi z)}	`BesselJ(nu + 1, z)HankelH2(nu, z)- BesselJ(nu, z)HankelH2(nu + 1, z) = - 2I/(Piz)`	`BesselJ[\[Nu]+ 1, z]HankelH2[\[Nu], z]- BesselJ[\[Nu], z]HankelH2[\[Nu]+ 1, z] == - 2I/(Piz)`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.5.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\HankelH{1}{\nu}@{z},\HankelH{2}{\nu}@{z}} = \HankelH{1}{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\HankelH{1}{\nu}@{z}\HankelH{2}{\nu+1}@{z}}	`(HankelH1(nu, z))diff(HankelH2(nu, z), z)-diff(HankelH1(nu, z), z)(HankelH2(nu, z)) = HankelH1(nu + 1, z)HankelH2(nu, z)- HankelH1(nu, z)HankelH2(nu + 1, z)`	`Wronskian[{HankelH1[\[Nu], z], HankelH2[\[Nu], z]}, z] == HankelH1[\[Nu]+ 1, z]HankelH2[\[Nu], z]- HankelH1[\[Nu], z]HankelH2[\[Nu]+ 1, z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.5.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu+1}@{z}\HankelH{2}{\nu}@{z}-\HankelH{1}{\nu}@{z}\HankelH{2}{\nu+1}@{z} = -4i/(\pi z)}	`HankelH1(nu + 1, z)HankelH2(nu, z)- HankelH1(nu, z)HankelH2(nu + 1, z) = - 4I/(Piz)`	`HankelH1[\[Nu]+ 1, z]HankelH2[\[Nu], z]- HankelH1[\[Nu], z]HankelH2[\[Nu]+ 1, z] == - 4I/(Piz)`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.6#E3X	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselJ{0}'@{z} = -\BesselJ{1}@{z}}	`diff( BesselJ(0, z), z$(1) ) = - BesselJ(1, z)`	`D[BesselJ[0, z], {z, 1}] == - BesselJ[1, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#E3X	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselY{0}'@{z} = -\BesselY{1}@{z}}	`diff( BesselY(0, z), z$(1) ) = - BesselY(1, z)`	`D[BesselY[0, z], {z, 1}] == - BesselY[1, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#E3Xa	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{1}{0}'@{z} = -\HankelH{1}{1}@{z}}	`diff( HankelH1(0, z), z$(1) ) = - HankelH1(1, z)`	`D[HankelH1[0, z], {z, 1}] == - HankelH1[1, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#E3Xa	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{2}{0}'@{z} = -\HankelH{2}{1}@{z}}	`diff( HankelH2(0, z), z$(1) ) = - HankelH2(1, z)`	`D[HankelH2[0, z], {z, 1}] == - HankelH2[1, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{\nu-1}(z)+f_{\nu+1}(z) = (2\nu/\lambda)z^{-q}f_{\nu}(z)}	`f[nu - 1](z)+ f[nu + 1](z) = (2nu/ lambda) (z)^(- q)* f[nu]*(z)`	`Subscript[f, \[Nu]- 1](z)+ Subscript[f, \[Nu]+ 1](z) == (2\[Nu]/ \[Lambda]) (z)^(- q)* Subscript[f, \[Nu]]*(z)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu+1}-p_{\nu-1} = -\frac{2\nu}{a}q_{\nu}-\frac{2\nu}{b}r_{\nu}}	`p[nu + 1]- p[nu - 1] = -(2nu)/(a)q[nu]-(2nu)/(b)r[nu]`	`Subscript[p, \[Nu]+ 1]- Subscript[p, \[Nu]- 1] == -Divide[2\[Nu],a]Subscript[q, \[Nu]]-Divide[2\[Nu],b]Subscript[r, \[Nu]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{\nu+1}+r_{\nu} = \frac{\nu}{a}p_{\nu}-\frac{\nu+1}{b}p_{\nu+1}}	`q[nu + 1]+ r[nu] = (nu)/(a)p[nu]-(nu + 1)/(b)p[nu + 1]`	`Subscript[q, \[Nu]+ 1]+ Subscript[r, \[Nu]] == Divide[\[Nu],a]Subscript[p, \[Nu]]-Divide[\[Nu]+ 1,b]Subscript[p, \[Nu]+ 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{\nu+1}+q_{\nu} = \frac{\nu}{b}p_{\nu}-\frac{\nu+1}{a}p_{\nu+1}}	`r[nu + 1]+ q[nu] = (nu)/(b)p[nu]-(nu + 1)/(a)p[nu + 1]`	`Subscript[r, \[Nu]+ 1]+ Subscript[q, \[Nu]] == Divide[\[Nu],b]Subscript[p, \[Nu]]-Divide[\[Nu]+ 1,a]Subscript[p, \[Nu]+ 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6#Ex18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{\nu} = \tfrac{1}{2}p_{\nu+1}+\tfrac{1}{2}p_{\nu-1}-\frac{\nu^{2}}{ab}p_{\nu}}	`s[nu] = (1)/(2)p[nu + 1]+(1)/(2)p[nu - 1]-((nu)^(2))/(ab)p[nu]`	`Subscript[s, \[Nu]] == Divide[1,2]Subscript[p, \[Nu]+ 1]+Divide[1,2]Subscript[p, \[Nu]- 1]-Divide[\[Nu]^(2),ab]Subscript[p, \[Nu]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.6.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu}s_{\nu}-q_{\nu}r_{\nu} = 4/(\pi^{2}ab)}	`p[nu]s[nu]- q[nu]r[nu] = 4/((Pi)^(2)* a*b)`	`Subscript[p, \[Nu]]Subscript[s, \[Nu]]- Subscript[q, \[Nu]]Subscript[r, \[Nu]] == 4/((Pi)^(2)* a*b)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.8.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{z} = -\frac{(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+\frac{2}{\pi}\ln@{\tfrac{1}{2}z}\BesselJ{n}@{z}-\frac{(\tfrac{1}{2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(\digamma@{k+1}+\digamma@{n+k+1})\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}}	`BesselY(n, z) = -(((1)/(2)z)^(- n))/(Pi)sum((factorial(n - k - 1))/(factorial(k))((1)/(4)(z)^(2))^(k), k = 0..n - 1)+(2)/(Pi)ln((1)/(2)z)BesselJ(n, z)-(((1)/(2)z)^(n))/(Pi)sum((Psi(k + 1)+ Psi(n + k + 1))((-(1)/(4)(z)^(2))^(k))/(factorial(k)factorial(n + k)), k = 0..infinity)`	`BesselY[n, z] == -Divide[(Divide[1,2]z)^(- n),Pi]Sum[Divide[(n - k - 1)!,(k)!](Divide[1,4](z)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]Log[Divide[1,2]z]BesselJ[n, z]-Divide[(Divide[1,2]z)^(n),Pi]Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])Divide[(-Divide[1,4](z)^(2))^(k),(k)!(n + k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [6 / 21] {Plus[-0.4244131815783875, Times[0.4244131815783876, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[32, 3], Power[1.5, -6], Plus[3, Times[Rational[1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]} `Plus[-0.8841941282883073, Times[0.3183098861837907, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]]`
10.8.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\dotsi\right)}	`BesselY(0, z) = (2)/(Pi)(ln((1)/(2)z)+ gamma)* BesselJ(0, z)+(2)/(Pi)(((1)/(4)(z)^(2))/((factorial(1))^(2))-(1 +(1)/(2))(((1)/(4)(z)^(2))^(2))/((factorial(2))^(2))+(1 +(1)/(2)+(1)/(3))(((1)/(4)(z)^(2))^(3))/((factorial(3))^(2))- .. )`	`BesselY[0, z] == Divide[2,Pi](Log[Divide[1,2]z]+ EulerGamma)* BesselJ[0, z]+Divide[2,Pi](Divide[Divide[1,4](z)^(2),((1)!)^(2)]-(1 +Divide[1,2])Divide[(Divide[1,4](z)^(2))^(2),((2)!)^(2)]+(1 +Divide[1,2]+Divide[1,3])Divide[(Divide[1,4](z)^(2))^(3),((3)!)^(2)]- \[Ellipsis])`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[0.08653583575184755, 0.12491815695491987], Times[-0.6366197723675814, Plus[Complex[0.13592303240740744, 0.19620888054491187], Times[-1.0, …]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.07160606681826986, -0.15074612001799426], Times[-0.6366197723675814, Plus[Complex[-0.11248553240740736, -0.23680382134730746], Times[-1.0, …]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.8.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\mu}@{z} = (\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}\EulerGamma@{\mu+k+1}}}	`BesselJ(nu, z)BesselJ(mu, z) = ((1)/(2)z)^(nu + mu)* sum((nu + mu + k + 1[k](-(1)/(4)(z)^(2))^(k))/(factorial(k)GAMMA(nu + k + 1)GAMMA(mu + k + 1)), k = 0..infinity)`	`BesselJ[\[Nu], z]BesselJ[\[Mu], z] == (Divide[1,2]z)^(\[Nu]+ \[Mu])* Sum[Divide[Subscript[\[Nu]+ \[Mu]+ k + 1, k](-Divide[1,4](z)^(2))^(k),(k)!Gamma[\[Nu]+ k + 1]Gamma[\[Mu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [300 / 300] {Plus[Complex[0.18482793500467376, -0.06270111308873656], Times[Complex[-0.17426361621858172, -0.037827155645948574], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -2], Subscript[Plus[1, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], k]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} `Plus[Complex[0.47215054540190965, -0.036453907426047115], Times[Complex[-0.27630938504679325, 0.26010894184513544], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -1], Power[Gamma[Plus[1, P`
10.9.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta}}	`BesselJ(0, z) = (1)/(Pi)int(cos(zsin(theta)), theta = 0..Pi)`	`BesselJ[0, z] == Divide[1,Pi]Integrate[Cos[zSin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Successful	Successful	-	Failed [4 / 7] `{Complex[0.1024204169391214, -0.20298051839359257] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.35155242920280916, 0.2300320660405755] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.9.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}\diff{\theta}}	`(1)/(Pi)int(cos(zsin(theta)), theta = 0..Pi) = (1)/(Pi)int(cos(zcos(theta)), theta = 0..Pi)`	`Divide[1,Pi]Integrate[Cos[zSin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]Integrate[Cos[zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 7]
10.9.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta}}	`BesselJ(n, z) = (1)/(Pi)int(cos(zsin(theta)- n*theta), theta = 0..Pi)`	`BesselJ[n, z] == Divide[1,Pi]Integrate[Cos[zSin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 7]	Successful [Tested: 7]
10.9.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta} = \frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\cos@{n\theta}\diff{\theta}}	`(1)/(Pi)int(cos(zsin(theta)- ntheta), theta = 0..Pi) = ((I)^(- n))/(Pi)int(exp(Izcos(theta))cos(ntheta), theta = 0..Pi)`	`Divide[1,Pi]Integrate[Cos[zSin[\[Theta]]- n\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(I)^(- n),Pi]Integrate[Exp[IzCos[\[Theta]]]Cos[n\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 7]	Skipped - Because timed out
10.9.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{4}{\pi^{2}}\int_{0}^{\frac{1}{2}\pi}\cos@{z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z\sin^{2}@@{\theta}}\right)\diff{\theta}}	`BesselY(0, z) = (4)/((Pi)^(2))int(cos(zcos(theta))(gamma + ln(2z(sin(theta))^(2))), theta = 0..(1)/(2)Pi)`	`BesselY[0, z] == Divide[4,(Pi)^(2)]Integrate[Cos[zCos[\[Theta]]](EulerGamma + Log[2z(Sin[\[Theta]])^(2)]), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None]`	Aborted	Aborted	Successful [Tested: 7]	Skipped - Because timed out
10.9.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}}	`BesselJ(nu, z) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(cos(zcos(theta))(sin(theta))^(2nu), theta = 0..Pi)`	`BesselJ[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Cos[zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]`	Error	Successful	-	Failed [20 / 35] `{Complex[0.009683985979314524, -0.05759180507972181] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.21993206762171735, 0.08917811286212163] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}`
10.9.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\cos@{zt}\diff{t}}	`(((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(cos(zcos(theta))(sin(theta))^(2nu), theta = 0..Pi) = (2((1)/(2)z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))int((1 - (t)^(2))^(nu -(1)/(2)) cos(z*t), t = 0..1)`	`Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Cos[zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[2(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2]) Cos[z*t], {t, 0, 1}, GenerateConditions->None]`	Error	Successful	-	Successful [Tested: 35]
10.9.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\left(\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}-\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}\right)}	`BesselY(nu, z) = (2((1)/(2)z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))(int((1 - (t)^(2))^(nu -(1)/(2)) sin(zt), t = 0..1)- int(exp(- zt)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity))`	`BesselY[\[Nu], z] == Divide[2(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]](Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2]) Sin[zt], {t, 0, 1}, GenerateConditions->None]- Integrate[Exp[- zt]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}, GenerateConditions->None])`	Successful	Successful	-	Failed [15 / 25] `{Complex[-0.9495382353861556, 0.46093572348323536] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1.5]}` `Complex[-0.7706973036767981, 0.20650772012904162] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 0.5]}`
10.9.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}-\nu t}\diff{t}}	`BesselJ(nu, z) = (1)/(Pi)int(cos(zsin(theta)- nutheta), theta = 0..Pi)-(sin(nuPi))/(Pi)int(exp(- zsinh(t)- nu*t), t = 0..infinity)`	`BesselJ[\[Nu], z] == Divide[1,Pi]Integrate[Cos[zSin[\[Theta]]- \[Nu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]Pi],Pi]Integrate[Exp[- zSinh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Failed [1 / 50] `1/50]: [[-.1812319652 <- {nu = -1/2, z = 3/2}`	Skipped - Because timed out
10.9.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t}+e^{-\nu t}\cos@{\nu\pi}\right)e^{-z\sinh@@{t}}\diff{t}}	`BesselY(nu, z) = (1)/(Pi)int(sin(zsin(theta)- nutheta), theta = 0..Pi)-(1)/(Pi)int((exp(nut)+ exp(- nut)cos(nuPi))* exp(- z*sinh(t)), t = 0..infinity)`	`BesselY[\[Nu], z] == Divide[1,Pi]Integrate[Sin[zSin[\[Theta]]- \[Nu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[1,Pi]Integrate[(Exp[\[Nu]t]+ Exp[- \[Nu]t]Cos[\[Nu]Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}}	`BesselJ(nu, x) = (2)/(Pi)int(sin(xcosh(t)-(1)/(2)nuPi)cosh(nut), t = 0..infinity)`	`BesselJ[\[Nu], x] == Divide[2,Pi]Integrate[Sin[xCosh[t]-Divide[1,2]\[Nu]Pi]Cosh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}}	`BesselY(nu, x) = -(2)/(Pi)int(cos(xcosh(t)-(1)/(2)nuPi)cosh(nut), t = 0..infinity)`	`BesselY[\[Nu], x] == -Divide[2,Pi]Integrate[Cos[xCosh[t]-Divide[1,2]\[Nu]Pi]Cosh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}}\diff{t}}	`BesselJ(0, x) = (2)/(Pi)int(sin(xcosh(t)), t = 0..infinity)`	`BesselJ[0, x] == Divide[2,Pi]Integrate[Sin[xCosh[t]], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}}\diff{t}}	`BesselY(0, x) = -(2)/(Pi)int(cos(xcosh(t)), t = 0..infinity)`	`BesselY[0, x] == -Divide[2,Pi]Integrate[Cos[xCosh[t]], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{e^{-\frac{1}{2}\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{iz\cosh@@{t}-\nu t}\diff{t}}	`HankelH1(nu, z) = (exp(-(1)/(2)nuPiI))/(PiI)int(exp(Izcosh(t)- nut), t = - infinity..infinity)`	`HankelH1[\[Nu], z] == Divide[Exp[-Divide[1,2]\[Nu]PiI],PiI]Integrate[Exp[IzCosh[t]- \[Nu]t], {t, - Infinity, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = -\frac{e^{\frac{1}{2}\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh@@{t}-\nu t}\diff{t}}	`HankelH2(nu, z) = -(exp((1)/(2)nuPiI))/(PiI)int(exp(- Izcosh(t)- nut), t = - infinity..infinity)`	`HankelH2[\[Nu], z] == -Divide[Exp[Divide[1,2]\[Nu]PiI],PiI]Integrate[Exp[- IzCosh[t]- \[Nu]t], {t, - Infinity, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\sin@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}}	`BesselJ(nu, x) = (2((1)/(2)x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))int((sin(xt))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity)`	`BesselJ[\[Nu], x] == Divide[2(Divide[1,2]x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]Integrate[Divide[Sin[xt],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None]`	Successful	Aborted	-	Successful [Tested: 15]
10.9#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{x} = -\frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}}	`BesselY(nu, x) = -(2((1)/(2)x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))int((cos(xt))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity)`	`BesselY[\[Nu], x] == -Divide[2(Divide[1,2]x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]Integrate[Divide[Cos[xt],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None]`	Successful	Aborted	-	Skip - No test values generated
10.9.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\BesselJ{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos@@{\theta}}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-\zeta\cosh@@{t}-z\sinh@@{t}-\nu t}\diff{t}}	`((z + zeta)/(z - zeta))^((1)/(2)nu) BesselJ(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = (1)/(Pi)int(exp(zetacos(theta))cos(zsin(theta)- nutheta), theta = 0..Pi)-(sin(nuPi))/(Pi)int(exp(- zetacosh(t)- zsinh(t)- nut), t = 0..infinity)`	`(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]\[Nu]) BesselJ[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == Divide[1,Pi]Integrate[Exp[\[Zeta]Cos[\[Theta]]]Cos[zSin[\[Theta]]- \[Nu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]Pi],Pi]Integrate[Exp[- \[Zeta]Cosh[t]- zSinh[t]- \[Nu]t], {t, 0, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\BesselY{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos@@{\theta}}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t+\zeta\cosh@@{t}}+e^{-\nu t-\zeta\cosh@@{t}}\cos@{\nu\pi}\right)\*e^{-z\sinh@@{t}}\diff{t}}	`((z + zeta)/(z - zeta))^((1)/(2)nu) BesselY(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = (1)/(Pi)int(exp(zetacos(theta))sin(zsin(theta)- nutheta), theta = 0..Pi)-(1)/(Pi)int((exp(nut + zetacosh(t))+ exp(- nut - zetacosh(t))cos(nuPi))* exp(- z*sinh(t)), t = 0..infinity)`	`(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]\[Nu]) BesselY[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == Divide[1,Pi]Integrate[Exp[\[Zeta]Cos[\[Theta]]]Sin[zSin[\[Theta]]- \[Nu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[1,Pi]Integrate[(Exp[\[Nu]t + \[Zeta]Cosh[t]]+ Exp[- \[Nu]t - \[Zeta]Cosh[t]]Cos[\[Nu]Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\HankelH{1}{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi i}e^{-\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{iz\cosh@@{t}+i\zeta\sinh@@{t}-\nu t}\diff{t}}	`((z + zeta)/(z - zeta))^((1)/(2)nu) HankelH1(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = (1)/(PiI)exp(-(1)/(2)nuPiI)int(exp(Izcosh(t)+ Izetasinh(t)- nu*t), t = - infinity..infinity)`	`(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]\[Nu]) HankelH1[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == Divide[1,PiI]Exp[-Divide[1,2]\[Nu]PiI]Integrate[Exp[IzCosh[t]+ I\[Zeta]Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\HankelH{2}{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = -\frac{1}{\pi i}e^{\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh@@{t}-i\zeta\sinh@@{t}-\nu t}\diff{t}}	`((z + zeta)/(z - zeta))^((1)/(2)nu) HankelH2(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = -(1)/(PiI)exp((1)/(2)nuPiI)int(exp(- Izcosh(t)- Izetasinh(t)- nu*t), t = - infinity..infinity)`	`(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]\[Nu]) HankelH2[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == -Divide[1,PiI]Exp[Divide[1,2]\[Nu]PiI]Integrate[Exp[- IzCosh[t]- I\[Zeta]Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-\pi i}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}}	`BesselJ(nu, z) = (1)/(2PiI)int(exp(zsinh(t)- nut), t = infinity - PiI..infinity + Pi*I)`	`BesselJ[\[Nu], z] == Divide[1,2PiI]Integrate[Exp[zSinh[t]- \[Nu]t], {t, Infinity - PiI, Infinity + Pi*I}, GenerateConditions->None]`	Error	Failure	-	Failed [70 / 70] `{Complex[0.4358908643715884, -0.07192294931339177] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.0679098760861825, 0.09257666026367889] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.9#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{1}{\pi i}\int_{-\infty}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}}	`HankelH1(nu, z) = (1)/(PiI)int(exp(zsinh(t)- nut), t = - infinity..infinity + Pi*I)`	`HankelH1[\[Nu], z] == Divide[1,PiI]Integrate[Exp[zSinh[t]- \[Nu]t], {t, - Infinity, Infinity + Pi*I}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = -\frac{1}{\pi i}\int_{-\infty}^{\infty-\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}}	`HankelH2(nu, z) = -(1)/(PiI)int(exp(zsinh(t)- nut), t = - infinity..infinity - Pi*I)`	`HankelH2[\[Nu], z] == -Divide[1,PiI]Integrate[Exp[zSinh[t]- \[Nu]t], {t, - Infinity, Infinity - Pi*I}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.9.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{2\pi i}\int_{-\infty}^{(0+)}\exp@{t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}}	`BesselJ(nu, z) = (((1)/(2)z)^(nu))/(2PiI)int(exp(t -((z)^(2))/(4t))(1)/((t)^(nu + 1)), t = - infinity..(0 +))`	`BesselJ[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],2PiI]Integrate[Exp[t -Divide[(z)^(2),4t]]Divide[1,(t)^(\[Nu]+ 1)], {t, - Infinity, (0 +)}, GenerateConditions->None]`	Error	Failure	-	Error
10.9.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{\EulerGamma@{\frac{1}{2}-\nu}(\frac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{0}^{(1+)}\cos@{zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}}	`BesselJ(nu, z) = (GAMMA((1)/(2)- nu)((1)/(2)z)^(nu))/((Pi)^((3)/(2))* I)int(cos(zt)*((t)^(2)- 1)^(nu -(1)/(2)), t = 0..(1 +))`	`BesselJ[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]](Divide[1,2]z)^\[Nu],(Pi)^(Divide[3,2])* I]Integrate[Cos[zt]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 0, (1 +)}, GenerateConditions->None]`	Error	Failure	-	Error
10.9#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1+i\infty}^{(1+)}e^{izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}}	`HankelH1(nu, z) = (GAMMA((1)/(2)- nu)((1)/(2)z)^(nu))/((Pi)^((3)/(2))* I)int(exp(Izt)((t)^(2)- 1)^(nu -(1)/(2)), t = 1 + I*infinity..(1 +))`	`HankelH1[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]](Divide[1,2]z)^\[Nu],(Pi)^(Divide[3,2])* I]Integrate[Exp[Izt]((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 + I*Infinity, (1 +)}, GenerateConditions->None]`	Error	Failure	-	Error
10.9#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1-i\infty}^{(1+)}e^{-izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}}	`HankelH2(nu, z) = (GAMMA((1)/(2)- nu)((1)/(2)z)^(nu))/((Pi)^((3)/(2))* I)int(exp(- Izt)((t)^(2)- 1)^(nu -(1)/(2)), t = 1 - I*infinity..(1 +))`	`HankelH2[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]](Divide[1,2]z)^\[Nu],(Pi)^(Divide[3,2])* I]Integrate[Exp[- Izt]((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 - I*Infinity, (1 +)}, GenerateConditions->None]`	Error	Failure	-	Error
10.9.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{x} = \frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\EulerGamma@{-t}(\tfrac{1}{2}x)^{\nu+2t}}{\EulerGamma@{\nu+t+1}}\diff{t}}	`BesselJ(nu, x) = (1)/(2PiI)int((GAMMA(- t)((1)/(2)x)^(nu + 2t))/(GAMMA(nu + t + 1)), t = - Iinfinity..Iinfinity)`	`BesselJ[\[Nu], x] == Divide[1,2PiI]Integrate[Divide[Gamma[- t](Divide[1,2]x)^(\[Nu]+ 2t),Gamma[\[Nu]+ t + 1]], {t, - IInfinity, IInfinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{-\infty-ic}^{-\infty+ic}\frac{\EulerGamma@{t}}{\EulerGamma@{\nu-t+1}}(\tfrac{1}{2}z)^{\nu-2t}\diff{t}}	`BesselJ(nu, z) = (1)/(2PiI)int((GAMMA(t))/(GAMMA(nu - t + 1))((1)/(2)z)^(nu - 2t), t = - infinity - Ic..- infinity + Ic)`	`BesselJ[\[Nu], z] == Divide[1,2PiI]Integrate[Divide[Gamma[t],Gamma[\[Nu]- t + 1]](Divide[1,2]z)^(\[Nu]- 2t), {t, - Infinity - Ic, - Infinity + Ic}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [300 / 300] `{Complex[0.4358908643715884, -0.07192294931339177] <- {Rule[c, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.0679098760861825, 0.09257666026367889] <- {Rule[c, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.9.E24	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{z} = -\frac{e^{-\frac{1}{2}\nu\pi i}}{2\pi^{2}}\*\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(-\tfrac{1}{2}iz)^{\nu-2t}\diff{t}}	`HankelH1(nu, z) = -(exp(-(1)/(2)nuPiI))/(2(Pi)^(2))* int(GAMMA(t)GAMMA(t - nu)(-(1)/(2)Iz)^(nu - 2t), t = c - Iinfinity..c + I*infinity)`	`HankelH1[\[Nu], z] == -Divide[Exp[-Divide[1,2]\[Nu]PiI],2(Pi)^(2)]* Integrate[Gamma[t]Gamma[t - \[Nu]](-Divide[1,2]Iz)^(\[Nu]- 2t), {t, c - IInfinity, c + I*Infinity}, GenerateConditions->None]`	Failure	Aborted	Failed [120 / 120] `120/120]: [[.2971181619-.8401954886I <- {c = -3/2, nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `-.8661908042+.2691615148I <- {c = -3/2, nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}`	Skipped - Because timed out
10.9.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{z} = \frac{e^{\frac{1}{2}\nu\pi i}}{2\pi^{2}}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}iz)^{\nu-2t}\diff{t}}	`HankelH2(nu, z) = (exp((1)/(2)nuPiI))/(2(Pi)^(2))int(GAMMA(t)GAMMA(t - nu)((1)/(2)Iz)^(nu - 2t), t = c - Iinfinity..c + Iinfinity)`	`HankelH2[\[Nu], z] == Divide[Exp[Divide[1,2]\[Nu]PiI],2(Pi)^(2)]Integrate[Gamma[t]Gamma[t - \[Nu]](Divide[1,2]Iz)^(\[Nu]- 2t), {t, c - IInfinity, c + IInfinity}, GenerateConditions->None]`	Failure	Aborted	Failed [120 / 120] `120/120]: [[-.1414870617+.1246394392I <- {c = -3/2, nu = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)}` `-.1498748781e-1-.1846515642I <- {c = -3/2, nu = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I}`	Skipped - Because timed out
10.9.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\mu}@{z}\BesselJ{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}}	`BesselJ(mu, z)BesselJ(nu, z) = (2)/(Pi)int(BesselJ(mu + nu, 2zcos(theta))cos((mu - nu) theta), theta = 0..Pi/ 2)`	`BesselJ[\[Mu], z]BesselJ[\[Nu], z] == Divide[2,Pi]Integrate[BesselJ[\[Mu]+ \[Nu], 2zCos[\[Theta]]]Cos[(\[Mu]- \[Nu]) \[Theta]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None]`	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.9.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{2\nu}@{2(z\zeta)^{\frac{1}{2}}\sin@@{\theta}}\cos@{(z-\zeta)\cos@@{\theta}}\diff{\theta}}	`BesselJ(nu, z)BesselJ(nu, zeta) = (2)/(Pi)int(BesselJ(2nu, 2(zzeta)^((1)/(2)) sin(theta))cos((z - zeta) cos(theta)), theta = 0..Pi/ 2)`	`BesselJ[\[Nu], z]BesselJ[\[Nu], \[Zeta]] == Divide[2,Pi]Integrate[BesselJ[2\[Nu], 2(z\[Zeta])^(Divide[1,2]) Sin[\[Theta]]]Cos[(z - \[Zeta]) Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None]`	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.9.E28	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp@{\frac{1}{2}t-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselI{\nu}@{\frac{z\zeta}{t}}\frac{\diff{t}}{t}}	`BesselJ(nu, z)BesselJ(nu, zeta) = (1)/(2PiI)int(* exp((1)/(2)t -((z)^(2)+ (zeta)^(2))/(2t))BesselI(nu, (zzeta)/(t))(1)/(t), t = c - Iinfinity..c + I*infinity)`	`BesselJ[\[Nu], z]BesselJ[\[Nu], \[Zeta]] == Divide[1,2PiI]Integrate[* Exp[Divide[1,2]t -Divide[(z)^(2)+ \[Zeta]^(2),2t]]BesselI[\[Nu], Divide[z\[Zeta],t]]Divide[1,t], {t, c - IInfinity, c + I*Infinity}, GenerateConditions->None]`	Error	Failure	-	Error
10.9.E29	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\mu}@{x}\BesselJ{\nu}@{x} = \frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\EulerGamma@{-t}\EulerGamma@{2t+\mu+\nu+1}(\tfrac{1}{2}x)^{\mu+\nu+2t}}{\EulerGamma@{t+\mu+1}\EulerGamma@{t+\nu+1}\EulerGamma@{t+\mu+\nu+1}}\diff{t}}	`BesselJ(mu, x)BesselJ(nu, x) = (1)/(2PiI)int((GAMMA(- t)GAMMA(2t + mu + nu + 1)((1)/(2)x)^(mu + nu + 2t))/(GAMMA(t + mu + 1)GAMMA(t + nu + 1)GAMMA(t + mu + nu + 1)), t = - Iinfinity..I*infinity)`	`BesselJ[\[Mu], x]BesselJ[\[Nu], x] == Divide[1,2PiI]Integrate[Divide[Gamma[- t]Gamma[2t + \[Mu]+ \[Nu]+ 1](Divide[1,2]x)^(\[Mu]+ \[Nu]+ 2t),Gamma[t + \[Mu]+ 1]Gamma[t + \[Nu]+ 1]Gamma[t + \[Mu]+ \[Nu]+ 1]], {t, - IInfinity, I*Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.9.E30	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}^{2}@{z}+\BesselY{\nu}^{2}@{z} = \frac{8}{\pi^{2}}\int_{0}^{\infty}\cosh@{2\nu t}\modBesselK{0}@{2z\sinh@@{t}}\diff{t}}	`(BesselJ(nu, z))^(2)+ (BesselY(nu, z))^(2) = (8)/((Pi)^(2))int(cosh(2nut)BesselK(0, 2zsinh(t)), t = 0..infinity)`	`(BesselJ[\[Nu], z])^(2)+ (BesselY[\[Nu], z])^(2) == Divide[8,(Pi)^(2)]Integrate[Cosh[2\[Nu]t]BesselK[0, 2zSinh[t]], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.11.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\BesselJ{\nu}@{z}}	`BesselJ(nu, zexp(mPiI)) = exp(mnuPiI)*BesselJ(nu, z)`	`BesselJ[\[Nu], zExp[mPiI]] == Exp[m\[Nu]PiI]*BesselJ[\[Nu], z]`	Failure	Failure	Failed [132 / 210] `132/210]: [[-1.978604450-.5916012221I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `.4256613630-.5580360922e-1I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [120 / 210] `{Complex[-1.9786044502778974, -0.5916012230349773] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.42566136315461117, -0.05580360945599949] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\BesselY{\nu}@{z}+2i\sin@{m\nu\pi}\cot@{\nu\pi}\BesselJ{\nu}@{z}}	`BesselY(nu, zexp(mPiI)) = exp(- mnuPiI)BesselY(nu, z)+ 2Isin(mnuPi)cot(nuPi)BesselJ(nu, z)`	`BesselY[\[Nu], zExp[mPiI]] == Exp[- m\[Nu]PiI]BesselY[\[Nu], z]+ 2ISin[m\[Nu]Pi]Cot[\[Nu]Pi]BesselJ[\[Nu], z]`	Failure	Failure	Failed [170 / 210] `170/210]: [[-4.492502702+3.271310776I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `19.72399963+2.416868418I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [162 / 210] `{Complex[-4.49250270148862, 3.2713107749000305] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[19.723999620348792, 2.416868461226219] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\nu\pi}\HankelH{1}{\nu}@{ze^{m\pi i}} = -\sin@{(m-1)\nu\pi}\HankelH{1}{\nu}@{z}-e^{-\nu\pi i}\sin@{m\nu\pi}\HankelH{2}{\nu}@{z}}	`sin(nuPi)HankelH1(nu, zexp(mPiI)) = - sin((m - 1) nuPi)HankelH1(nu, z)- exp(- nuPiI)sin(mnuPi)HankelH2(nu, z)`	`Sin[\[Nu]Pi]HankelH1[\[Nu], zExp[mPiI]] == - Sin[(m - 1) \[Nu]Pi]HankelH1[\[Nu], z]- Exp[- \[Nu]PiI]Sin[m\[Nu]Pi]HankelH2[\[Nu], z]`	Failure	Failure	Failed [132 / 210] `132/210]: [[-16.06107638+5.815014709I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `39.27071892+24.34608468I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [120 / 210] `{Complex[-16.061076381218605, 5.815014694873561] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[39.27071883811536, 24.346084784539414] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\nu\pi}\HankelH{2}{\nu}@{ze^{m\pi i}} = e^{\nu\pi i}\sin@{m\nu\pi}\HankelH{1}{\nu}@{z}+\sin@{(m+1)\nu\pi}\HankelH{2}{\nu}@{z}}	`sin(nuPi)HankelH2(nu, zexp(mPiI)) = exp(nuPiI)sin(mnuPi)HankelH1(nu, z)+ sin((m + 1) nuPi)HankelH2(nu, z)`	`Sin[\[Nu]Pi]HankelH2[\[Nu], zExp[mPiI]] == Exp[\[Nu]PiI]Sin[m\[Nu]Pi]HankelH1[\[Nu], z]+ Sin[(m + 1) \[Nu]Pi]HankelH2[\[Nu], z]`	Failure	Failure	Failed [132 / 210] `132/210]: [[9.518923666+1.283901315I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `-38.63237633-26.24866521I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [120 / 210] `{Complex[9.518923662743454, 1.2839013369012835] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-38.63237622058036, -26.24866530437453] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\nu}@{ze^{\pi i}} = -e^{-\nu\pi i}\HankelH{2}{\nu}@{z}}	`HankelH1(nu, zexp(PiI)) = - exp(- nuPiI)*HankelH2(nu, z)`	`HankelH1[\[Nu], zExp[PiI]] == - Exp[- \[Nu]PiI]*HankelH2[\[Nu], z]`	Failure	Failure	Failed [20 / 70] `20/70]: [[-5.249915228-5.084103922I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `-3.129030441-5.176244122I <- {nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}`	Failed [20 / 70] `{Complex[-5.2499152251779275, -5.084103924523598] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.4609763579335797, 35.01102127779514] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.11#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\nu}@{ze^{-\pi i}} = -e^{\nu\pi i}\HankelH{1}{\nu}@{z}}	`HankelH2(nu, zexp(- PiI)) = - exp(nuPiI)*HankelH1(nu, z)`	`HankelH2[\[Nu], zExp[- PiI]] == - Exp[\[Nu]PiI]*HankelH1[\[Nu], z]`	Failure	Failure	Failed [50 / 70] `50/70]: [[1.033334476+.7163604616I <- {nu = 1/23^(1/2)+1/2I, z = 1/2-1/2I3^(1/2)}` `1.427918302+.5187414665I <- {nu = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I}`	Failed [50 / 70] `{Complex[1.0333344760783634, 0.7163604618419928] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.538721989873022, -0.29666827540401164] <- {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.11.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{ze^{m\pi i}} = (-1)^{mn}(\BesselY{n}@{z}+2im\BesselJ{n}@{z})}	`BesselY(n, zexp(mPiI)) = (- 1)^(mn)(BesselY(n, z)+ 2ImBesselJ(n, z))`	`BesselY[n, zExp[mPiI]] == (- 1)^(mn)(BesselY[n, z]+ 2ImBesselJ[n, z])`	Failure	Failure	Failed [57 / 63] `57/63]: [[-.7553141392+1.723217630I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 1}` `.3969469092-.2695422112I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 2}`	Failed [48 / 63] `{Complex[-0.7553141389736522, 1.7232176296930342] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.39694690825884216, -0.26954221211204654] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{n}@{ze^{m\pi i}} = (-1)^{mn-1}((m-1)\HankelH{1}{n}@{z}+m\HankelH{2}{n}@{z})}	`HankelH1(n, zexp(mPiI)) = (- 1)^(mn - 1)((m - 1)HankelH1(n, z)+ m*HankelH2(n, z))`	`HankelH1[n, zExp[mPiI]] == (- 1)^(mn - 1)((m - 1)HankelH1[n, z]+ m*HankelH2[n, z])`	Failure	Failure	Failed [57 / 63] `57/63]: [[-1.723217630-.7553141394I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 1}` `.2695422111+.3969469092I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 2}`	Failed [48 / 63] `{Complex[-1.7232176296930342, -0.7553141389736522] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.26954221211204654, 0.39694690825884216] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{n}@{ze^{m\pi i}} = (-1)^{mn}(m\HankelH{1}{n}@{z}+(m+1)\HankelH{2}{n}@{z})}	`HankelH2(n, zexp(mPiI)) = (- 1)^(mn)(mHankelH1(n, z)+(m + 1)*HankelH2(n, z))`	`HankelH2[n, zExp[mPiI]] == (- 1)^(mn)(mHankelH1[n, z]+(m + 1)*HankelH2[n, z])`	Failure	Failure	Failed [57 / 63] `57/63]: [[1.723217630+.755314139I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 1}` `-.269542211-.396946909I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 2}`	Failed [48 / 63] `{Complex[1.7232176296930342, 0.7553141389736524] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.26954221211204654, -0.39694690825884216] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.11#E9X	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselJ{\nu}@{\conj{z}} = \conj{\BesselJ{\nu}@{z}}}	`BesselJ(nu, conjugate(z)) = conjugate(BesselJ(nu, z))`	`BesselJ[\[Nu], Conjugate[z]] == Conjugate[BesselJ[\[Nu], z]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.11#E9X	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\BesselY{\nu}@{\conj{z}} = \conj{\BesselY{\nu}@{z}}}	`BesselY(nu, conjugate(z)) = conjugate(BesselY(nu, z))`	`BesselY[\[Nu], Conjugate[z]] == Conjugate[BesselY[\[Nu], z]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.11#E9Xa	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{1}{\nu}@{\conj{z}} = \conj{\HankelH{2}{\nu}@{z}}}	`HankelH1(nu, conjugate(z)) = conjugate(HankelH2(nu, z))`	`HankelH1[\[Nu], Conjugate[z]] == Conjugate[HankelH2[\[Nu], z]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.11#E9Xa	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\HankelH{2}{\nu}@{\conj{z}} = \conj{\HankelH{1}{\nu}@{z}}}	`HankelH2(nu, conjugate(z)) = conjugate(HankelH1(nu, z))`	`HankelH2[\[Nu], Conjugate[z]] == Conjugate[HankelH1[\[Nu], z]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.12.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\frac{1}{2}z(t-t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\BesselJ{m}@{z}}	`exp((1)/(2)z(t - (t)^(- 1))) = sum((t)^(m)* BesselJ(m, z), m = - infinity..infinity)`	`Exp[Divide[1,2]z(t - (t)^(- 1))] == Sum[(t)^(m)* BesselJ[m, z], {m, - Infinity, Infinity}, GenerateConditions->None]`	Failure	Successful	Successful [Tested: 42]	Successful [Tested: 42]
10.12#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z\sin@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}\BesselJ{2k}@{z}\cos@{2k\theta}}	`cos(zsin(theta)) = BesselJ(0, z)+ 2sum(BesselJ(2k, z)cos(2ktheta), k = 1..infinity)`	`Cos[zSin[\[Theta]]] == BesselJ[0, z]+ 2Sum[BesselJ[2k, z]Cos[2k\[Theta]], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Successful	Skipped - Because timed out	Successful [Tested: 70]
10.12#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z\sin@@{\theta}} = 2\sum_{k=0}^{\infty}\BesselJ{2k+1}@{z}\sin@{(2k+1)\theta}}	`sin(zsin(theta)) = 2sum(BesselJ(2k + 1, z)sin((2k + 1) theta), k = 0..infinity)`	`Sin[zSin[\[Theta]]] == 2Sum[BesselJ[2k + 1, z]Sin[(2k + 1) \[Theta]], {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Successful	Skipped - Because timed out	Successful [Tested: 70]
10.12#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z\cos@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{2k}@{z}\cos@{2k\theta}}	`cos(zcos(theta)) = BesselJ(0, z)+ 2sum((- 1)^(k)* BesselJ(2k, z)cos(2ktheta), k = 1..infinity)`	`Cos[zCos[\[Theta]]] == BesselJ[0, z]+ 2Sum[(- 1)^(k)* BesselJ[2k, z]Cos[2k\[Theta]], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Successful	Skipped - Because timed out	Successful [Tested: 70]
10.12#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z\cos@@{\theta}} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{2k+1}@{z}\cos@{(2k+1)\theta}}	`sin(zcos(theta)) = 2sum((- 1)^(k)* BesselJ(2k + 1, z)cos((2k + 1) theta), k = 0..infinity)`	`Sin[zCos[\[Theta]]] == 2Sum[(- 1)^(k)* BesselJ[2k + 1, z]Cos[(2k + 1) \[Theta]], {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Successful	Skipped - Because timed out	Successful [Tested: 70]
10.12.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 = \BesselJ{0}@{z}+2\BesselJ{2}@{z}+2\BesselJ{4}@{z}+2\BesselJ{6}@{z}+\dotsb}	`1 = BesselJ(0, z)+ 2BesselJ(2, z)+ 2BesselJ(4, z)+ 2*BesselJ(6, z)+ ..`	`1 == BesselJ[0, z]+ 2BesselJ[2, z]+ 2BesselJ[4, z]+ 2*BesselJ[6, z]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-9.924736618779559^-8, -1.6360842739013975^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-9.440290587615918^-8, -1.7199789187696823^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.12#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \BesselJ{0}@{z}-2\BesselJ{2}@{z}+2\BesselJ{4}@{z}-2\BesselJ{6}@{z}+\dotsb}	`cos(z) = BesselJ(0, z)- 2BesselJ(2, z)+ 2BesselJ(4, z)- 2*BesselJ(6, z)+ ..`	`Cos[z] == BesselJ[0, z]- 2BesselJ[2, z]+ 2BesselJ[4, z]- 2*BesselJ[6, z]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-9.976125969757277^-8, -1.6267640928768756^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-9.384008414770051^-8, -1.7292990711625933^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.12#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = 2\BesselJ{1}@{z}-2\BesselJ{3}@{z}+2\BesselJ{5}@{z}-\dotsb}	`sin(z) = 2BesselJ(1, z)- 2BesselJ(3, z)+ 2*BesselJ(5, z)- ..`	`Sin[z] == 2BesselJ[1, z]- 2BesselJ[3, z]+ 2*BesselJ[5, z]- \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[2.683443869444524^-6, 1.443280323643048^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[1.6585570595806232^-6, -2.68341820086615^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.12#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}z\cos@@{z} = \BesselJ{1}@{z}-9\BesselJ{3}@{z}+25\BesselJ{5}@{z}-49\BesselJ{7}@{z}+\dotsb}	`(1)/(2)zcos(z) = BesselJ(1, z)- 9BesselJ(3, z)+ 25BesselJ(5, z)- 49*BesselJ(7, z)+ ..`	`Divide[1,2]zCos[z] == BesselJ[1, z]- 9BesselJ[3, z]+ 25BesselJ[5, z]- 49*BesselJ[7, z]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-1.0583928733431947^-8, -4.2969798588234076^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[4.4207480831559565^-7, 1.0857586385526474^-8], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.12#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}z\sin@@{z} = 4\BesselJ{2}@{z}-16\BesselJ{4}@{z}+36\BesselJ{6}@{z}-\dotsi}	`(1)/(2)zsin(z) = 4BesselJ(2, z)- 16BesselJ(4, z)+ 36*BesselJ(6, z)- ..`	`Divide[1,2]zSin[z] == 4BesselJ[2, z]- 16BesselJ[4, z]+ 36*BesselJ[6, z]- \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[3.196945008165919^-6, 5.1972576656234^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[2.997776089863624^-6, 5.542144419168338^-6], …] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.13.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w^{(2n)} = (-1)^{n}\lambda^{2n}z^{-n}w}	`(w)^(2n) = (- 1)^(n) (lambda)^(2n) (z)^(- n)* w`	`(w)^(2n) == (- 1)^(n) \[Lambda]^(2n) (z)^(- n)* w`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.13.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2}+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w = 0}	`((vartheta)^(4)- 2((nu)^(2)+ (mu)^(2))(vartheta)^(2)+((nu)^(2)- (mu)^(2))^(2))* w + 4(z)^(2)(vartheta + 1)(vartheta + 2) w = 0`	`(\[CurlyTheta]^(4)- 2(\[Nu]^(2)+ \[Mu]^(2))\[CurlyTheta]^(2)+(\[Nu]^(2)- \[Mu]^(2))^(2))* w + 4(z)^(2)(\[CurlyTheta]+ 1)(\[CurlyTheta]+ 2) w == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.14#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{\nu}@{x}\| \leq 1}	`abs(BesselJ(nu, x)) <= 1`	`Abs[BesselJ[\[Nu], x]] <= 1`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.14#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{\nu}@{x}\| \leq 2^{-\frac{1}{2}}}	`abs(BesselJ(nu, x)) <= (2)^(-(1)/(2))`	`Abs[BesselJ[\[Nu], x]] <= (2)^(-Divide[1,2])`	Failure	Failure	Successful [Tested: 2]	Successful [Tested: 2]
10.14.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \BesselJ{\nu}@{\nu}}	`0 < BesselJ(nu, nu)`	`0 < BesselJ[\[Nu], \[Nu]]`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.14.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{\nu} < \frac{2^{\frac{1}{3}}}{3^{\frac{2}{3}}\EulerGamma@{\tfrac{2}{3}}\nu^{\frac{1}{3}}}}	`BesselJ(nu, nu) < ((2)^((1)/(3)))/((3)^((2)/(3))* GAMMA((2)/(3))*(nu)^((1)/(3)))`	`BesselJ[\[Nu], \[Nu]] < Divide[(2)^(Divide[1,3]),(3)^(Divide[2,3])* Gamma[Divide[2,3]]*\[Nu]^(Divide[1,3])]`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.14.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{n}@{z}\| \leq e^{\|\imagpart@@{z}\|}}	`abs(BesselJ(n, z)) <= exp(abs(Im(z)))`	`Abs[BesselJ[n, z]] <= Exp[Abs[Im[z]]]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.14.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{\nu}@{z}\| \leq \frac{\|\tfrac{1}{2}z\|^{\nu}e^{\|\imagpart@@{z}\|}}{\EulerGamma@{\nu+1}}}	`abs(BesselJ(nu, z)) <= ((abs((1)/(2)z))^(nu) exp(abs(Im(z))))/(GAMMA(nu + 1))`	`Abs[BesselJ[\[Nu], z]] <= Divide[(Abs[Divide[1,2]z])^\[Nu] Exp[Abs[Im[z]]],Gamma[\[Nu]+ 1]]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.14.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{\nu}@{\nu x}\| \leq \frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}}	`abs(BesselJ(nu, nux)) <= ((x)^(nu) exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu))`	`Abs[BesselJ[\[Nu], \[Nu]x]] <= Divide[(x)^\[Nu] Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^\[Nu]]`	Failure	Failure	Successful [Tested: 3]	Skip - No test values generated
10.14.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{\nu}'@{\nu x}\| \leq \frac{(1+x^{2})^{\frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\frac{x^{\nu}\exp@{\nu(1-x^{2})^{\frac{1}{2}}}}{\left(1+(1-x^{2})^{\frac{1}{2}}\right)^{\nu}}}	`abs(diff( BesselJ(nu, nux), nux$(1) )) <= ((1 + (x)^(2))^((1)/(4)))/(x(2Pinu)^((1)/(2)))((x)^(nu)* exp(nu*(1 - (x)^(2))^((1)/(2))))/((1 +(1 - (x)^(2))^((1)/(2)))^(nu))`	`Abs[D[BesselJ[\[Nu], \[Nu]x], {\[Nu]x, 1}]] <= Divide[(1 + (x)^(2))^(Divide[1,4]),x(2Pi\[Nu])^(Divide[1,2])]Divide[(x)^\[Nu]* Exp[\[Nu]*(1 - (x)^(2))^(Divide[1,2])],(1 +(1 - (x)^(2))^(Divide[1,2]))^\[Nu]]`	Error	Failure	-	Skip - No test values generated
10.14.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 \leq \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}}}	`1 <= (BesselJ(nu, nux))/((x)^(nu) BesselJ(nu, nu))`	`1 <= Divide[BesselJ[\[Nu], \[Nu]x],(x)^\[Nu] BesselJ[\[Nu], \[Nu]]]`	Failure	Failure	Successful [Tested: 3]	Skip - No test values generated
10.14.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\BesselJ{\nu}@{\nu x}}{x^{\nu}\BesselJ{\nu}@{\nu}} \leq e^{\nu(1-x)}}	`(BesselJ(nu, nux))/((x)^(nu) BesselJ(nu, nu)) <= exp(nu*(1 - x))`	`Divide[BesselJ[\[Nu], \[Nu]x],(x)^\[Nu] BesselJ[\[Nu], \[Nu]]] <= Exp[\[Nu]*(1 - x)]`	Failure	Failure	Successful [Tested: 3]	Skip - No test values generated
10.14.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{n}@{nz}\| \leq \frac{\left\|z^{n}\exp@{n(1-z^{2})^{\frac{1}{2}}}\right\|}{\left\|1+(1-z^{2})^{\frac{1}{2}}\right\|^{n}}}	`abs(BesselJ(n, nz)) <= (abs((z)^(n) exp(n*(1 - (z)^(2))^((1)/(2)))))/((abs(1 +(1 - (z)^(2))^((1)/(2))))^(n))`	`Abs[BesselJ[n, nz]] <= Divide[Abs[(z)^(n) Exp[n*(1 - (z)^(2))^(Divide[1,2])]],(Abs[1 +(1 - (z)^(2))^(Divide[1,2])])^(n)]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.14.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\BesselJ{n}@{nz}\| \leq 1}	`abs(BesselJ(n, n*z)) <= 1`	`Abs[BesselJ[n, n*z]] <= 1`	Failure	Failure	Error	Successful [Tested: 21]
10.15.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselJ{+\nu}@{z}}{\nu} = +\BesselJ{+\nu}@{z}\ln@{\tfrac{1}{2}z}-(\tfrac{1}{2}z)^{+\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{k+1+\nu}}{\EulerGamma@{k+1+\nu}}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!}}	`diff(BesselJ(+ nu, z), nu) = + BesselJ(+ nu, z)ln((1)/(2)z)-((1)/(2)z)^(+ nu) sum((- 1)^(k)(Psi(k + 1 + nu))/(GAMMA(k + 1 + nu))(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity)`	`D[BesselJ[+ \[Nu], z], \[Nu]] == + BesselJ[+ \[Nu], z]Log[Divide[1,2]z]-(Divide[1,2]z)^(+ \[Nu]) Sum[(- 1)^(k)Divide[PolyGamma[k + 1 + \[Nu]],Gamma[k + 1 + \[Nu]]]Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [7 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -2]}`
10.15.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselJ{-\nu}@{z}}{\nu} = -\BesselJ{-\nu}@{z}\ln@{\tfrac{1}{2}z}+(\tfrac{1}{2}z)^{-\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{k+1-\nu}}{\EulerGamma@{k+1-\nu}}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!}}	`diff(BesselJ(- nu, z), nu) = - BesselJ(- nu, z)ln((1)/(2)z)+((1)/(2)z)^(- nu) sum((- 1)^(k)(Psi(k + 1 - nu))/(GAMMA(k + 1 - nu))(((1)/(4)*(z)^(2))^(k))/(factorial(k)), k = 0..infinity)`	`D[BesselJ[- \[Nu], z], \[Nu]] == - BesselJ[- \[Nu], z]Log[Divide[1,2]z]+(Divide[1,2]z)^(- \[Nu]) Sum[(- 1)^(k)Divide[PolyGamma[k + 1 - \[Nu]],Gamma[k + 1 - \[Nu]]]Divide[(Divide[1,4]*(z)^(2))^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [7 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 2]}`
10.15.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\BesselY{\nu}@{z}}{\nu} = \cot@{\nu\pi}\left(\pderiv{\BesselJ{\nu}@{z}}{\nu}-\pi\BesselY{\nu}@{z}\right)-\csc@{\nu\pi}\pderiv{\BesselJ{-\nu}@{z}}{\nu}-\pi\BesselJ{\nu}@{z}}	`diff(BesselY(nu, z), nu) = cot(nuPi)(diff(BesselJ(nu, z), nu)- PiBesselY(nu, z))- csc(nuPi)diff(BesselJ(- nu, z), nu)- PiBesselJ(nu, z)`	`D[BesselY[\[Nu], z], \[Nu]] == Cot[\[Nu]Pi](D[BesselJ[\[Nu], z], \[Nu]]- PiBesselY[\[Nu], z])- Csc[\[Nu]Pi]D[BesselJ[- \[Nu], z], \[Nu]]- PiBesselJ[\[Nu], z]`	Successful	Failure	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.16#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{1}{2}}@{z} = \BesselY{-\frac{1}{2}}@{z}}	`BesselJ((1)/(2), z) = BesselY(-(1)/(2), z)`	`BesselJ[Divide[1,2], z] == BesselY[-Divide[1,2], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.16#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sin@@{z}}	`BesselY(-(1)/(2), z) = ((2)/(Piz))^((1)/(2)) sin(z)`	`BesselY[-Divide[1,2], z] == (Divide[2,Piz])^(Divide[1,2]) Sin[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.16#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-\frac{1}{2}}@{z} = -\BesselY{\frac{1}{2}}@{z}}	`BesselJ(-(1)/(2), z) = - BesselY((1)/(2), z)`	`BesselJ[-Divide[1,2], z] == - BesselY[Divide[1,2], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.16#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\BesselY{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\cos@@{z}}	`- BesselY((1)/(2), z) = ((2)/(Piz))^((1)/(2)) cos(z)`	`- BesselY[Divide[1,2], z] == (Divide[2,Piz])^(Divide[1,2]) Cos[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.16#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{1}{\frac{1}{2}}@{z} = -i\HankelH{1}{-\frac{1}{2}}@{z}}	`HankelH1((1)/(2), z) = - I*HankelH1(-(1)/(2), z)`	`HankelH1[Divide[1,2], z] == - I*HankelH1[-Divide[1,2], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.16#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -i\HankelH{1}{-\frac{1}{2}}@{z} = -i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{iz}}	`- IHankelH1(-(1)/(2), z) = - I((2)/(Piz))^((1)/(2)) exp(I*z)`	`- IHankelH1[-Divide[1,2], z] == - I(Divide[2,Piz])^(Divide[1,2]) Exp[I*z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.16#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelH{2}{\frac{1}{2}}@{z} = i\HankelH{2}{-\frac{1}{2}}@{z}}	`HankelH2((1)/(2), z) = I*HankelH2(-(1)/(2), z)`	`HankelH2[Divide[1,2], z] == I*HankelH2[-Divide[1,2], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.16#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle i\HankelH{2}{-\frac{1}{2}}@{z} = i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{-iz}}	`IHankelH2(-(1)/(2), z) = I((2)/(Piz))^((1)/(2)) exp(- I*z)`	`IHankelH2[-Divide[1,2], z] == I(Divide[2,Piz])^(Divide[1,2]) Exp[- I*z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.16#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{1}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(\paraW@{0}{2z^{\frac{1}{2}}}-\paraW@{0}{-2z^{\frac{1}{2}}}\right)}	`Error`	BesselJ[Divide[1,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[1,4])(Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] * Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), 2(z)^(Divide[1,2]) * Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), 2(z)^(Divide[1,2]) * Exp[Divide[PiI,4]]] )- Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] * Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), - 2(z)^(Divide[1,2]) * Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), - 2(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] ))	Missing Macro Error	Failure	-	Failed [7 / 7] {Plus[Complex[0.8427727646508262, -0.04212015747529019], Times[Complex[0.4703662267003617, -0.06192488852586185], Plus[Times[0.4550898605622274, Plus[Times[Complex[0.3150667711363517, -1.1318933470332309], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.1941072423227021, 0.35884759380625464], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[1.684848183162187, 0.4798071226199044], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.8058077119758371, -1.0109338182195815], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} `Plus[Complex[0.7942814592773979, 0.6544287188687908], Times[Complex[`
10.16#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-\frac{1}{4}}@{z} = 2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(\paraW@{0}{2z^{\frac{1}{2}}}+\paraW@{0}{-2z^{\frac{1}{2}}}\right)}	`Error`	BesselJ[-Divide[1,4], z] == (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[1,4])(Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] * Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), 2(z)^(Divide[1,2]) * Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), 2(z)^(Divide[1,2]) * Exp[Divide[PiI,4]]] )+ Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] * Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), - 2(z)^(Divide[1,2]) * Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), - 2(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] ))	Missing Macro Error	Aborted	-	Failed [7 / 7] {Plus[Complex[0.7570692040611657, -0.36205959587261455], Times[Complex[-0.4703662267003617, 0.06192488852586186], Plus[Times[0.4550898605622274, Plus[Times[Complex[0.3150667711363517, -1.1318933470332309], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.1941072423227021, 0.35884759380625464], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[1.684848183162187, 0.4798071226199044], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.8058077119758371, -1.0109338182195815], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} `Plus[Complex[1.1199640481676587, -0.30003362129733535], Times[Complex`
10.16#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}-\paraW'@{0}{-2z^{\frac{1}{2}}}\right)}	`Error`	BesselJ[Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])((D[Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] * Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), temp Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), temp Exp[Divide[PiI,4]]] ), {temp, 1}]/.temp-> 2(z)^(Divide[1,2]))- (D[Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), temp Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), temp Exp[Divide[PiI,4]]] ), {temp, 1}]/.temp-> - 2(z)^(Divide[1,2])))	Missing Macro Error	Failure	-	Failed [7 / 7] {Plus[Complex[0.5824093961234496, 0.15854248220296385], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAM
10.16#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{-\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}+\paraW'@{0}{-2z^{\frac{1}{2}}}\right)}	`Error`	BesselJ[-Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])((D[Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] * Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), temp Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), temp Exp[Divide[PiI,4]]] ), {temp, 1}]/.temp-> 2(z)^(Divide[1,2]))+ (D[Sqrt[(Sqrt[1+Exp[2Pi(0)]]-Exp[Pi(0)])/2] Exp[Divide[Pi(0),4]] ( Exp[I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] * ParabolicCylinderD[- 1/2 - I(0), temp Exp[-Divide[PiI,4]]] + Exp[-I(Pi/8 + Arg[GAMMA[1/2 + I(0)]]/2)] ParabolicCylinderD[- 1/2 + I(0), temp Exp[Divide[PiI,4]]] ), {temp, 1}]/.temp-> - 2(z)^(Divide[1,2])))	Missing Macro Error	Failure	-	Failed [7 / 7] {Plus[Complex[0.05605283808026881, -0.4145839244466886], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAM
10.16.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2iz}}	`BesselJ(nu, z) = (((1)/(2)z)^(nu) exp(- Iz))/(GAMMA(nu + 1))KummerM(nu +(1)/(2), 2nu + 1, + 2I*z)`	`BesselJ[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu] Exp[- Iz],Gamma[\[Nu]+ 1]]Hypergeometric1F1[\[Nu]+Divide[1,2], 2\[Nu]+ 1, + 2I*z]`	Failure	Successful	Failed [7 / 56] `7/56]: [[-.827986137e-1+.7317301038I <- {nu = -1/2, z = 1/23^(1/2)+1/2I}` `-.8060140108+.3257248263I <- {nu = -1/2, z = -1/2+1/2I3^(1/2)}`	Failed [7 / 56] `{Complex[-0.08279861346468581, 0.7317301035002939] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}` `Complex[-0.8060140105131326, 0.32572482654389856] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]}`
10.16.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{+ iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{- 2iz}}	`BesselJ(nu, z) = (((1)/(2)z)^(nu) exp(+ Iz))/(GAMMA(nu + 1))KummerM(nu +(1)/(2), 2nu + 1, - 2I*z)`	`BesselJ[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu] Exp[+ Iz],Gamma[\[Nu]+ 1]]Hypergeometric1F1[\[Nu]+Divide[1,2], 2\[Nu]+ 1, - 2I*z]`	Failure	Successful	Failed [7 / 56] `7/56]: [[.827986132e-1-.7317301035I <- {nu = -1/2, z = 1/23^(1/2)+1/2I}` `.8060140102-.3257248264I <- {nu = -1/2, z = -1/2+1/2I3^(1/2)}`	Failed [7 / 56] `{Complex[0.08279861346468548, -0.7317301035002935] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}` `Complex[0.8060140105131325, -0.325724826543898] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]}`
10.16.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{e^{-(2\nu+1)\pi i/4}}{2^{2\nu}\EulerGamma@{\nu+1}}(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{+ 2iz}}	`BesselJ(nu, z) = (exp(-(2nu + 1) PiI/ 4))/((2)^(2nu)* GAMMA(nu + 1))(2z)^(-(1)/(2))* WhittakerM(0, nu, + 2Iz)`	`BesselJ[\[Nu], z] == Divide[Exp[-(2\[Nu]+ 1) PiI/ 4],(2)^(2\[Nu])* Gamma[\[Nu]+ 1]](2z)^(-Divide[1,2])* WhittakerM[0, \[Nu], + 2Iz]`	Failure	Failure	Failed [1 / 7] `1/7]: [[1.448710179-.1398527410I <- {z = -1/2+1/2I*3^(1/2), nu = 1/4}`	Failed [1 / 7] `{Complex[1.448710178146189, -0.13985274040860685] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Rational[1, 4]]}`
10.16.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{e^{+(2\nu+1)\pi i/4}}{2^{2\nu}\EulerGamma@{\nu+1}}(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{- 2iz}}	`BesselJ(nu, z) = (exp(+(2nu + 1) PiI/ 4))/((2)^(2nu)* GAMMA(nu + 1))(2z)^(-(1)/(2))* WhittakerM(0, nu, - 2Iz)`	`BesselJ[\[Nu], z] == Divide[Exp[+(2\[Nu]+ 1) PiI/ 4],(2)^(2\[Nu])* Gamma[\[Nu]+ 1]](2z)^(-Divide[1,2])* WhittakerM[0, \[Nu], - 2Iz]`	Failure	Failure	Failed [1 / 7] `1/7]: [[1.191860674-.595668984e-1I <- {z = -1/23^(1/2)-1/2*I, nu = 1/4}`	Failed [1 / 7] `{Complex[1.191860673767867, -0.059566897950845576] <- {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Rational[1, 4]]}`
10.16.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+1}}\genhyperF{0}{1}@{-}{\nu+1}{-\tfrac{1}{4}z^{2}}}	`BesselJ(nu, z) = (((1)/(2)z)^(nu))/(GAMMA(nu + 1))hypergeom([-], [nu + 1], -(1)/(4)*(z)^(2))`	`BesselJ[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+ 1]]HypergeometricPFQ[{-}, {\[Nu]+ 1}, -Divide[1,4]*(z)^(2)]`	Error	Failure	-	Error
10.17.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{\frac{1}{2}} = \exp@{\tfrac{1}{2}\ln@@{\|z\|}+\tfrac{1}{2}i\phase@@{z}}}	`(z)^((1)/(2)) = exp((1)/(2)ln(abs(z))+(1)/(2)I*argument(z))`	`(z)^(Divide[1,2]) == Exp[Divide[1,2]Log[Abs[z]]+Divide[1,2]I*Arg[z]]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.17.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}}	`(exp(z)/(2Pi))GAMMA(p)GAMMA(1-p,z) = (exp(z))/(2Pi)GAMMA(p)GAMMA(1 - p, z)`	`Error`	Successful	Missing Macro Error	-	-
10.17.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}^{+}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(+ i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{- 2iz}+R_{m,\ell}^{+}(\nu,z)\right)}	`(R[ell])^(+)(nu , z) = (- 1)^(ell) 2cos(nuPi)(sum((+ I)^(k)(a[k](nu))/((z)^(k))(exp(- 2Iz)/(2Pi))GAMMA(ell - k)GAMMA(1-ell - k,- 2Iz), k = 0..m - 1)+ R(R[m , ell])^(+)*(nu , z))`	`Error`	Error	Missing Macro Error	-	-
10.17.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}^{-}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(- i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{+ 2iz}+R_{m,\ell}^{-}(\nu,z)\right)}	`(R[ell])^(-)(nu , z) = (- 1)^(ell) 2cos(nuPi)(sum((- I)^(k)(a[k](nu))/((z)^(k))(exp(+ 2Iz)/(2Pi))GAMMA(ell - k)GAMMA(1-ell - k,+ 2Iz), k = 0..m - 1)+ R(R[m , ell])^(-)*(nu , z))`	`Error`	Error	Missing Macro Error	-	-
10.18#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}}}	`Error`	`Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((BesselJ[\[Nu], x])^(2)+ (BesselY[\[Nu], x])^(2))^(Divide[1,2])`	Missing Macro Error	Failure	-	Failed [30 / 30] `{Complex[0.19554332981034928, -0.3390785475644471] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.7197518351343698, 1.0182547128018542] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.18#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}}}	`Error`	`Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((D[BesselJ[\[Nu], x], {x, 1}])^(2)+ (D[BesselY[\[Nu], x], {x, 1}])^(2))^(Divide[1,2])`	Missing Macro Error	Failure	-	Failed [30 / 30] `{Complex[-0.3065654786420606, 0.09106250304027241] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.41179972752410343, -0.08651542233456301] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.18.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x^{2}-\nu^{2})\HankelmodM{\nu}@{x}\HankelmodM{\nu}'@{x}+x^{2}\HankelmodderivN{\nu}@{x}\HankelmodderivN{\nu}'@{x}+x\HankelmodderivN{\nu}^{2}@{x} = 0}	`Error`	`((x)^(2)- \[Nu]^(2))* Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2]D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 1}]+ (x)^(2) Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]D[Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2], {x, 1}]+ x(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2) == 0`	Missing Macro Error	Aborted	-	Failed [30 / 30] `{Complex[0.7620133104065328, -0.7345190431210711] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-3.2607567755462643, -4.475082123070706] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.18.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\HankelmodM{\nu}''@{x}+x\HankelmodM{\nu}'@{x}+(x^{2}-\nu^{2})\HankelmodM{\nu}@{x} = \frac{4}{\pi^{2}{\HankelmodM{\nu}^{3}(x)}}}	`Error`	`(x)^(2)* D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 2}]+ xD[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 1}]+((x)^(2)- \[Nu]^(2)) Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == Divide[4,(Pi)^(2)*(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(3)]`	Missing Macro Error	Translation Error	-	-
10.20.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{\zeta}{z}\right)^{2} = \frac{1-z^{2}}{\zeta z^{2}}}	`(diff(zeta, z))^(2) = (1 - (z)^(2))/(zeta*(z)^(2))`	`(D[\[Zeta], z])^(2) == Divide[1 - (z)^(2),\[Zeta]*(z)^(2)]`	Failure	Failure	Failed [70 / 70] `70/70]: [[.8660254030+.4999999994I <- {z = 1/23^(1/2)+1/2I, zeta = 1/23^(1/2)+1/2I}` `.4999999994-.8660254030I <- {z = 1/23^(1/2)+1/2I, zeta = -1/2+1/2I3^(1/2)}`	Failed [70 / 70] `{Complex[0.8660254037844386, 0.4999999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.4999999999999999, -0.8660254037844386] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.20.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{3}\zeta^{\frac{3}{2}} = \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t}}	`(2)/(3)*(zeta)^((3)/(2)) = int((sqrt(1 - (t)^(2)))/(t), t = z..1)`	`Divide[2,3]*\[Zeta]^(Divide[3,2]) == Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.20.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t} = \ln@{\frac{1+\sqrt{1-z^{2}}}{z}}-\sqrt{1-z^{2}}}	`int((sqrt(1 - (t)^(2)))/(t), t = z..1) = ln((1 +sqrt(1 - (z)^(2)))/(z))-sqrt(1 - (z)^(2))`	`Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}, GenerateConditions->None] == Log[Divide[1 +Sqrt[1 - (z)^(2)],z]]-Sqrt[1 - (z)^(2)]`	Error	Aborted	-	Skipped - Because timed out
10.20.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{3}(-\zeta)^{\frac{3}{2}} = \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t}}	`(2)/(3)*(- zeta)^((3)/(2)) = int((sqrt((t)^(2)- 1))/(t), t = 1..z)`	`Divide[2,3]*(- \[Zeta])^(Divide[3,2]) == Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None]`	Failure	Aborted	Failed [20 / 20] `20/20]: [[-.7483698391+.4714045210I <- {z = 3/2, zeta = 1/23^(1/2)+1/2I}` `-.2769653183-.6666666667I <- {z = 3/2, zeta = -1/2+1/2I3^(1/2)}`	Failed [20 / 20] `{Complex[-0.7483698389729962, 0.4714045207910317] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.27696531818196457, -0.6666666666666666] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.20.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t} = \sqrt{z^{2}-1}-\asec@@{z}}	`int((sqrt((t)^(2)- 1))/(t), t = 1..z) = sqrt((z)^(2)- 1)- arcsec(z)`	`Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None] == Sqrt[(z)^(2)- 1]- ArcSec[z]`	Failure	Aborted	Successful [Tested: 2]	Successful [Tested: 2]
10.20#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{0}(0) = 1}	`A[0]*(0) = 1`	`Subscript[A, 0]*(0) == 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{1}(0) = -\tfrac{1}{225}}	`A[1]*(0) = -(1)/(225)`	`Subscript[A, 1]*(0) == -Divide[1,225]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{2}(0) = \tfrac{1\;51439}{2182\;95000}}	`A[2]*(0) = (151439)/(218295000)`	`Subscript[A, 2]*(0) == Divide[151439,218295000]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{3}(0) = -\tfrac{8872\;78009}{250\;49351\;25000}}	`A[3]*(0) = -(887278009)/(2504935125000)`	`Subscript[A, 3]*(0) == -Divide[887278009,2504935125000]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{0}(0) = \tfrac{1}{70}2^{\frac{1}{3}}}	`B[0](0) = (1)/(70)(2)^((1)/(3))`	`Subscript[B, 0](0) == Divide[1,70](2)^(Divide[1,3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1}(0) = -\tfrac{1213}{10\;23750}2^{\frac{1}{3}}}	`B[1](0) = -(1213)/(1023750)(2)^((1)/(3))`	`Subscript[B, 1](0) == -Divide[1213,1023750](2)^(Divide[1,3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2}(0) = \tfrac{1\;65425\;37833}{3774\;32055\;00000}2^{\frac{1}{3}}}	`B[2](0) = (16542537833)/(37743205500000)(2)^((1)/(3))`	`Subscript[B, 2](0) == Divide[16542537833,37743205500000](2)^(Divide[1,3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3}(0) = -\tfrac{959\;71711\;84603}{25\;47666\;37125\;00000}2^{\frac{1}{3}}}	`B[3](0) = -(9597171184603)/(25476663712500000)(2)^((1)/(3))`	`Subscript[B, 3](0) == -Divide[9597171184603,25476663712500000](2)^(Divide[1,3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = (\tfrac{3}{2})^{\frac{2}{3}}(\tau- i\pi)^{\frac{2}{3}}}	`zeta = ((3)/(2))^((2)/(3))(tau - IPi)^((2)/(3))`	`\[Zeta] == (Divide[3,2])^(Divide[2,3])(\[Tau]- IPi)^(Divide[2,3])`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = e^{- i\pi/3}\tau}	`zeta = exp(- IPi/ 3)tau`	`\[Zeta] == Exp[- IPi/ 3]\[Tau]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.20.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = +(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}+\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}}	`z = +(taucoth(tau)- (tau)^(2))^((1)/(2))+ I((tau)^(2)- tau*tanh(tau))^((1)/(2))`	`z == +(\[Tau]Coth[\[Tau]]- \[Tau]^(2))^(Divide[1,2])+ I(\[Tau]^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2])`	Failure	Failure	Failed [21 / 21] `21/21]: [[.8660254040-1.214547924I <- {tau = 3/2, z = 1/23^(1/2)+1/2I}` `-.5000000000-.8485225201I <- {tau = 3/2, z = -1/2+1/2I3^(1/2)}`	Skip - No test values generated
10.20.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = -(\tau\coth@@{\tau}-\tau^{2})^{\frac{1}{2}}-\iunit(\tau^{2}-\tau\tanh@@{\tau})^{\frac{1}{2}}}	`z = -(taucoth(tau)- (tau)^(2))^((1)/(2))- I((tau)^(2)- tau*tanh(tau))^((1)/(2))`	`z == -(\[Tau]Coth[\[Tau]]- \[Tau]^(2))^(Divide[1,2])- I(\[Tau]^(2)- \[Tau]*Tanh[\[Tau]])^(Divide[1,2])`	Failure	Failure	Failed [21 / 21] `21/21]: [[.8660254040+2.214547924I <- {tau = 3/2, z = 1/23^(1/2)+1/2I}` `-.5000000000+2.580573328I <- {tau = 3/2, z = -1/2+1/2I3^(1/2)}`	Skip - No test values generated
10.21#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{\nu}(0) = 0}	`rho[nu]*(0) = 0`	`Subscript[\[Rho], \[Nu]]*(0) == 0`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\rho_{\nu}^{2}\deriv{\rho_{\nu}}{t}\deriv[3]{\rho_{\nu}}{t}-3\rho_{\nu}^{2}\\left(\deriv[2]{\rho_{\nu}}{t}\right)^{2}-4\pi^{2}\rho_{\nu}^{2}\\left(\deriv{\rho_{\nu}}{t}\right)^{2}+(4\rho_{\nu}^{2}+1-4\nu^{2})\left(\deriv{\rho_{\nu}}{t}\right)^{4} = 0}	`2(rho[nu])^(2)diff(rho[nu], t)diff(rho[nu], [t$(3)])- 3(rho[nu])^(2)(diff(rho[nu], [t$(2)]))^(2)- 4(Pi)^(2)* (rho[nu])^(2)(diff(rho[nu], t))^(2)(4rho(rho[nu])^(2)+ 1 - 4(nu)^(2))(diff(rho[nu], t))^(4) = 0`	`2(Subscript[\[Rho], \[Nu]])^(2)D[Subscript[\[Rho], \[Nu]], t]D[Subscript[\[Rho], \[Nu]], {t, 3}]- 3(Subscript[\[Rho], \[Nu]])^(2)(D[Subscript[\[Rho], \[Nu]], {t, 2}])^(2)- 4(Pi)^(2)* (Subscript[\[Rho], \[Nu]])^(2)(D[Subscript[\[Rho], \[Nu]], t])^(2)(4\[Rho](Subscript[\[Rho], \[Nu]])^(2)+ 1 - 4\[Nu]^(2))(D[Subscript[\[Rho], \[Nu]], t])^(4) == 0`	Successful	Successful	-	Successful [Tested: 300]
10.21.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}}	`diff(c, nu) = 2cint(BesselK(0, 2csinh(t))exp(- 2nu*t), t = 0..infinity)`	`D[c, \[Nu]] == 2cIntegrate[BesselK[0, 2cSinh[t]]Exp[- 2\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.21#Ex19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{0} = 1}	`alpha[0] = 1`	`Subscript[\[Alpha], 0] == 1`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{1} = \alpha}	`alpha[1] = alpha`	`Subscript[\[Alpha], 1] == \[Alpha]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2} = \tfrac{3}{10}\alpha^{2}}	`alpha[2] = (3)/(10)*(alpha)^(2)`	`Subscript[\[Alpha], 2] == Divide[3,10]*\[Alpha]^(2)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{3} = -\tfrac{1}{350}\alpha^{3}+\tfrac{1}{70}}	`alpha[3] = -(1)/(350)*(alpha)^(3)+(1)/(70)`	`Subscript[\[Alpha], 3] == -Divide[1,350]*\[Alpha]^(3)+Divide[1,70]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{4} = -\tfrac{479}{63000}\alpha^{4}-\tfrac{1}{3150}\alpha}	`alpha[4] = -(479)/(63000)(alpha)^(4)-(1)/(3150)alpha`	`Subscript[\[Alpha], 4] == -Divide[479,63000]\[Alpha]^(4)-Divide[1,3150]\[Alpha]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex24	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{5} = \tfrac{20231}{80\;85000}\alpha^{5}-\tfrac{551}{1\;61700}\alpha^{2}}	`alpha[5] = (20231)/(8085000)(alpha)^(5)-(551)/(161700)(alpha)^(2)`	`Subscript[\[Alpha], 5] == Divide[20231,8085000]\[Alpha]^(5)-Divide[551,161700]\[Alpha]^(2)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21.E46	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \tfrac{1}{2}\ln@@{3}}	`a = (1)/(2)*ln(3)`	`a == Divide[1,2]*Log[3]`	Failure	Failure	Failed [6 / 6] `6/6]: [[-2.049306144 <- {a = -3/2}` `.9506938555 <- {a = 3/2}`	Failed [6 / 6] `{-2.049306144334055 <- {Rule[a, -1.5]}` `0.9506938556659451 <- {Rule[a, 1.5]}`
10.21.E46	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\ln@@{3} = 0.54931\dotsc}	`(1)/(2)*ln(3) = 0.54931 ..`	`Divide[1,2]*Log[3] == 0.54931 \[Ellipsis]`	Error	Failure	Skip - symbolical successful subtest	Failed [1 / 1] `{Plus[0.5493061443340549, Times[-0.54931, …]] <- {}`
10.21#Ex51	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{(m-1)\pi}{\lambda-1}}	`alpha = ((m - 1)* Pi)/(lambda - 1)`	`\[Alpha] == Divide[(m - 1)* Pi,\[Lambda]- 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex52	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{\mu+3}{8\lambda}}	`p = (mu + 3)/(8*lambda)`	`p == Divide[\[Mu]+ 3,8*\[Lambda]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex53	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = \frac{(\mu^{2}+46\mu-63)(\lambda^{3}-1)}{6(4\lambda)^{3}(\lambda-1)}}	`q = (((mu)^(2)+ 46mu - 63)((lambda)^(3)- 1))/(6(4lambda)^(3)*(lambda - 1))`	`q == Divide[(\[Mu]^(2)+ 46\[Mu]- 63)(\[Lambda]^(3)- 1),6(4\[Lambda])^(3)*(\[Lambda]- 1)]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex54	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)(\lambda^{5}-1)}{5(4\lambda)^{5}(\lambda-1)}}	`r = (((mu)^(3)+ 185(mu)^(2)- 2053mu + 1899)((lambda)^(5)- 1))/(5(4lambda)^(5)(lambda - 1))`	`r == Divide[(\[Mu]^(3)+ 185\[Mu]^(2)- 2053\[Mu]+ 1899)(\[Lambda]^(5)- 1),5(4\[Lambda])^(5)(\[Lambda]- 1)]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex55	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \frac{(m-\tfrac{1}{2})\pi}{\lambda-1}}	`alpha = ((m -(1)/(2))* Pi)/(lambda - 1)`	`\[Alpha] == Divide[(m -Divide[1,2])* Pi,\[Lambda]- 1]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex56	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = \frac{(\mu+3)\lambda-(\mu-1)}{8\lambda(\lambda-1)}}	`p = ((mu + 3)* lambda -(mu - 1))/(8lambda(lambda - 1))`	`p == Divide[(\[Mu]+ 3)* \[Lambda]-(\[Mu]- 1),8\[Lambda](\[Lambda]- 1)]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex57	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = \frac{(\mu^{2}+46\mu-63)\lambda^{3}-(\mu-1)(\mu-25)}{6(4\lambda)^{3}(\lambda-1)}}	`q = (((mu)^(2)+ 46mu - 63) (lambda)^(3)-(mu - 1)(mu - 25))/(6(4lambda)^(3)(lambda - 1))`	`q == Divide[(\[Mu]^(2)+ 46\[Mu]- 63) \[Lambda]^(3)-(\[Mu]- 1)(\[Mu]- 25),6(4\[Lambda])^(3)(\[Lambda]- 1)]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.21#Ex58	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \frac{(\mu^{3}+185\mu^{2}-2053\mu+1899)\lambda^{5}-(\mu-1)(\mu^{2}-114\mu+1073)}{5(4\lambda)^{5}(\lambda-1)}}	`r = (((mu)^(3)+ 185(mu)^(2)- 2053mu + 1899)* (lambda)^(5)-(mu - 1)((mu)^(2)- 114mu + 1073))/(5(4lambda)^(5)*(lambda - 1))`	`r == Divide[(\[Mu]^(3)+ 185\[Mu]^(2)- 2053\[Mu]+ 1899)* \[Lambda]^(5)-(\[Mu]- 1)(\[Mu]^(2)- 114\[Mu]+ 1073),5(4\[Lambda])^(5)*(\[Lambda]- 1)]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.22.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\diff{t} = 2\sum_{k=0}^{\infty}\BesselJ{\nu+2k+1}@{x}}	`int(BesselJ(nu, t), t = 0..x) = 2sum(BesselJ(nu + 2k + 1, x), k = 0..infinity)`	`Integrate[BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == 2Sum[BesselJ[\[Nu]+ 2k + 1, x], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Failed [2 / 24] `2/24]: [[-.277492396 <- {nu = -1/2, x = 3/2}` `-.1653166018 <- {nu = 1/2, x = 3/2}`	Skipped - Because timed out
10.22.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{2n}@{t}\diff{t} = \int_{0}^{x}\BesselJ{0}@{t}\diff{t}-2\sum_{k=0}^{n-1}\BesselJ{2k+1}@{x},\quad\int_{0}^{x}\BesselJ{2n+1}@{t}\diff{t}}	`int(BesselJ(2n, t), t = 0..x) = int(BesselJ(0, t), t = 0..x)- 2sum(BesselJ(2k + 1, x), k = 0..n - 1), int(BesselJ(2n + 1, t), t = 0..x)`	`Integrate[BesselJ[2n, t], {t, 0, x}, GenerateConditions->None] == Integrate[BesselJ[0, t], {t, 0, x}, GenerateConditions->None]- 2Sum[BesselJ[2k + 1, x], {k, 0, n - 1}, GenerateConditions->None], Integrate[BesselJ[2n + 1, t], {t, 0, x}, GenerateConditions->None]`	Failure	Failure	Error	Error
10.22.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{0}@{t}\diff{t}-2\sum_{k=0}^{n-1}\BesselJ{2k+1}@{x},\quad\int_{0}^{x}\BesselJ{2n+1}@{t}\diff{t} = 1-\BesselJ{0}@{x}-2\sum_{k=1}^{n}\BesselJ{2k}@{x}}	`int(BesselJ(0, t), t = 0..x)- 2sum(BesselJ(2k + 1, x), k = 0..n - 1), int(BesselJ(2n + 1, t), t = 0..x) = 1 - BesselJ(0, x)- 2sum(BesselJ(2*k, x), k = 1..n)`	`Integrate[BesselJ[0, t], {t, 0, x}, GenerateConditions->None]- 2Sum[BesselJ[2k + 1, x], {k, 0, n - 1}, GenerateConditions->None], Integrate[BesselJ[2n + 1, t], {t, 0, x}, GenerateConditions->None] == 1 - BesselJ[0, x]- 2Sum[BesselJ[2*k, x], {k, 1, n}, GenerateConditions->None]`	Failure	Failure	Error	Error
10.22.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = x^{\mu}\frac{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(\nu+2k+1)\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}+k}}{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{2}+k}}\BesselJ{\nu+2k+1}@{x}}	`int((t)^(mu)* BesselJ(nu, t), t = 0..x) = (x)^(mu)(GAMMA((1)/(2)nu +(1)/(2)mu +(1)/(2)))/(GAMMA((1)/(2)nu -(1)/(2)mu +(1)/(2))) sum(((nu + 2k + 1) GAMMA((1)/(2)nu -(1)/(2)mu +(1)/(2)+ k))/(GAMMA((1)/(2)nu +(1)/(2)mu +(3)/(2)+ k))BesselJ(nu + 2k + 1, x), k = 0..infinity)`	`Integrate[(t)^\[Mu]* BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == (x)^\[Mu]Divide[Gamma[Divide[1,2]\[Nu]+Divide[1,2]\[Mu]+Divide[1,2]],Gamma[Divide[1,2]\[Nu]-Divide[1,2]\[Mu]+Divide[1,2]]] Sum[Divide[(\[Nu]+ 2k + 1) Gamma[Divide[1,2]\[Nu]-Divide[1,2]\[Mu]+Divide[1,2]+ k],Gamma[Divide[1,2]\[Nu]+Divide[1,2]\[Mu]+Divide[3,2]+ k]]BesselJ[\[Nu]+ 2k + 1, x], {k, 0, Infinity}, GenerateConditions->None]`	Error	Failure	-	Skipped - Because timed out
10.22.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\BesselJ{k}@{x}}	`int((1 - BesselJ(0, t))/(t), t = 0..x) = (1)/(2)sum((Psi(k + 1)- Psi(1))/(factorial(k))((1)/(2)x)^(k) BesselJ(k, x), k = 1..infinity)`	`Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]Sum[Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!](Divide[1,2]x)^(k) BesselJ[k, x], {k, 1, Infinity}, GenerateConditions->None]`	Aborted	Failure	Successful [Tested: 3]	Failed [3 / 3] `{Plus[0.2622772441151432, Times[-0.5, NSum[Times[Power[0.75, k], BesselJ[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}` `Plus[0.03100698635091531, Times[-0.5, NSum[Times[Power[0.25, k], BesselJ[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}`
10.22.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = 2\sum_{k=0}^{\infty}(2k+3)(\digamma@{k+2}-\digamma@{1})\BesselJ{2k+3}@{x}}	`xint((1 - BesselJ(0, t))/(t), t = 0..x) = 2sum((2k + 3)(Psi(k + 2)- Psi(1))* BesselJ(2*k + 3, x), k = 0..infinity)`	`xIntegrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == 2Sum[(2k + 3)(PolyGamma[k + 2]- PolyGamma[1])* BesselJ[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 3]	Skipped - Because timed out
10.22.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sum_{k=0}^{\infty}(2k+3)(\digamma@{k+2}-\digamma@{1})\BesselJ{2k+3}@{x} = x-2\BesselJ{1}@{x}+2\sum_{k=0}^{\infty}(2k+5)\*(\digamma@{k+3}-\digamma@{1}-1)\BesselJ{2k+5}@{x}}	`2sum((2k + 3)(Psi(k + 2)- Psi(1)) BesselJ(2k + 3, x), k = 0..infinity) = x - 2BesselJ(1, x)+ 2sum((2k + 5)(Psi(k + 3)- Psi(1)- 1) BesselJ(2*k + 5, x), k = 0..infinity)`	`2Sum[(2k + 3)(PolyGamma[k + 2]- PolyGamma[1]) BesselJ[2k + 3, x], {k, 0, Infinity}, GenerateConditions->None] == x - 2BesselJ[1, x]+ 2Sum[(2k + 5)(PolyGamma[k + 3]- PolyGamma[1]- 1) BesselJ[2*k + 5, x], {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Aborted	Successful [Tested: 3]	Skipped - Because timed out
10.22.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}}	`int(BesselJ(2nu, 2zcos(theta))cos(2mutheta), theta = 0..(1)/(2)Pi) = (1)/(2)PiBesselJ(nu + mu, z)BesselJ(nu - mu, z)`	`Integrate[BesselJ[2\[Nu], 2zCos[\[Theta]]]Cos[2\[Mu]\[Theta]], {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[1,2]PiBesselJ[\[Nu]+ \[Mu], z]BesselJ[\[Nu]- \[Mu], z]`	Failure	Failure	Manual Skip!	Skipped - Because timed out
10.22.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \pi\cos@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}}	`int(BesselJ(2nu, 2zsin(theta))cos(2mutheta), theta = 0..Pi) = Picos(muPi)BesselJ(nu + mu, z)BesselJ(nu - mu, z)`	`Integrate[BesselJ[2\[Nu], 2zSin[\[Theta]]]Cos[2\[Mu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == PiCos[\[Mu]Pi]BesselJ[\[Nu]+ \[Mu], z]BesselJ[\[Nu]- \[Mu], z]`	Failure	Failure	Manual Skip!	Skipped - Because timed out
10.22.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\sin@{2\mu\theta}\diff{\theta} = \pi\sin@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}}	`int(BesselJ(2nu, 2zsin(theta))sin(2mutheta), theta = 0..Pi) = Pisin(muPi)BesselJ(nu + mu, z)BesselJ(nu - mu, z)`	`Integrate[BesselJ[2\[Nu], 2zSin[\[Theta]]]Sin[2\[Mu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == PiSin[\[Mu]Pi]BesselJ[\[Nu]+ \[Mu], z]BesselJ[\[Nu]- \[Mu], z]`	Failure	Failure	Manual Skip!	Skipped - Because timed out
10.22.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}^{2}@{z}}	`int(BesselJ(0, 2zsin(theta))cos(2ntheta), theta = 0..(1)/(2)Pi) = (1)/(2)Pi(BesselJ(n, z))^(2)`	`Integrate[BesselJ[0, 2zSin[\[Theta]]]Cos[2n\[Theta]], {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[1,2]Pi(BesselJ[n, z])^(2)`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.22.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\cot@{2\nu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}-\tfrac{1}{2}\pi\csc@{2\nu\pi}\BesselJ{\mu-\nu}@{z}\BesselJ{-\mu-\nu}@{z}}	`int(BesselY(2nu, 2zcos(theta))cos(2mutheta), theta = 0..(1)/(2)Pi) = (1)/(2)Picot(2nuPi)BesselJ(nu + mu, z)BesselJ(nu - mu, z)-(1)/(2)Picsc(2nuPi)BesselJ(mu - nu, z)*BesselJ(- mu - nu, z)`	`Integrate[BesselY[2\[Nu], 2zCos[\[Theta]]]Cos[2\[Mu]\[Theta]], {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[1,2]PiCot[2\[Nu]Pi]BesselJ[\[Nu]+ \[Mu], z]BesselJ[\[Nu]- \[Mu], z]-Divide[1,2]PiCsc[2\[Nu]Pi]BesselJ[\[Mu]- \[Nu], z]*BesselJ[- \[Mu]- \[Nu], z]`	Failure	Failure	Error	Skip - No test values generated
10.22.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}@{z}\BesselY{n}@{z}}	`int(BesselY(0, 2zsin(theta))cos(2ntheta), theta = 0..(1)/(2)Pi) = (1)/(2)PiBesselJ(n, z)*BesselY(n, z)`	`Integrate[BesselY[0, 2zSin[\[Theta]]]Cos[2n\[Theta]], {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[1,2]PiBesselJ[n, z]*BesselY[n, z]`	Failure	Failure	Successful [Tested: 7]	Skipped - Because timed out
10.22.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = 2^{\nu}\EulerGamma@{\nu+1}z^{-\nu-1}\BesselJ{\mu+\nu+1}@{z}}	`int(BesselJ(mu, zsin(theta))(sin(theta))^(mu + 1)(cos(theta))^(2nu + 1), theta = 0..(1)/(2)Pi) = (2)^(nu) GAMMA(nu + 1)(z)^(- nu - 1) BesselJ(mu + nu + 1, z)`	`Integrate[BesselJ[\[Mu], zSin[\[Theta]]](Sin[\[Theta]])^(\[Mu]+ 1)(Cos[\[Theta]])^(2\[Nu]+ 1), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == (2)^\[Nu] Gamma[\[Nu]+ 1](z)^(- \[Nu]- 1) BesselJ[\[Mu]+ \[Nu]+ 1, z]`	Successful	Aborted	-	Successful [Tested: 300]
10.22.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}^{2}@{\tfrac{1}{2}z}}	`int(BesselJ(mu, zsin(theta))(sin(theta))^(mu)(cos(theta))^(2mu), theta = 0..(1)/(2)Pi) = (Pi)^((1)/(2)) (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))(BesselJ(mu, (1)/(2)z))^(2)`	`Integrate[BesselJ[\[Mu], zSin[\[Theta]]](Sin[\[Theta]])^\[Mu](Cos[\[Theta]])^(2\[Mu]), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2]) (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]](BesselJ[\[Mu], Divide[1,2]z])^(2)`	Successful	Aborted	-	Successful [Tested: 35]
10.22.E21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselY{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}@{\tfrac{1}{2}z}\BesselY{\mu}@{\tfrac{1}{2}z}}	`int(BesselY(mu, zsin(theta))(sin(theta))^(mu)(cos(theta))^(2mu), theta = 0..(1)/(2)Pi) = (Pi)^((1)/(2)) (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))BesselJ(mu, (1)/(2)z)BesselY(mu, (1)/(2)z)`	`Integrate[BesselY[\[Mu], zSin[\[Theta]]](Sin[\[Theta]])^\[Mu](Cos[\[Theta]])^(2\[Mu]), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2]) (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]BesselJ[\[Mu], Divide[1,2]z]BesselY[\[Mu], Divide[1,2]z]`	Successful	Aborted	-	Skipped - Because timed out
10.22.E22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = \frac{\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}\BesselJ{\mu+\nu+\frac{1}{2}}@{z}}{(8\pi z)^{\frac{1}{2}}\EulerGamma@{\mu+\nu+1}}}	`int(BesselJ(mu, z(sin(theta))^(2))BesselJ(nu, z(cos(theta))^(2))(sin(theta))^(2mu + 1)(cos(theta))^(2nu + 1), theta = 0..(1)/(2)Pi) = (GAMMA(mu +(1)/(2))GAMMA(nu +(1)/(2))BesselJ(mu + nu +(1)/(2), z))/((8Piz)^((1)/(2))* GAMMA(mu + nu + 1))`	`Integrate[BesselJ[\[Mu], z(Sin[\[Theta]])^(2)]BesselJ[\[Nu], z(Cos[\[Theta]])^(2)](Sin[\[Theta]])^(2\[Mu]+ 1)(Cos[\[Theta]])^(2\[Nu]+ 1), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[Gamma[\[Mu]+Divide[1,2]]Gamma[\[Nu]+Divide[1,2]]BesselJ[\[Mu]+ \[Nu]+Divide[1,2], z],(8Piz)^(Divide[1,2])* Gamma[\[Mu]+ \[Nu]+ 1]]`	Error	Aborted	-	Skipped - Because timed out
10.22.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\alpha-1}\sec@@{\theta}\diff{\theta} = \frac{(\mu+\nu+\alpha)\EulerGamma@{\mu+\alpha}2^{\alpha-1}}{\nu\EulerGamma@{\mu+1}z^{\alpha}}\BesselJ{\mu+\nu+\alpha}@{z}}	`int(BesselJ(mu, z(sin(theta))^(2))BesselJ(nu, z(cos(theta))^(2))(sin(theta))^(2alpha - 1) sec(theta), theta = 0..(1)/(2)Pi) = ((mu + nu + alpha) GAMMA(mu + alpha)(2)^(alpha - 1))/(nuGAMMA(mu + 1)(z)^(alpha))BesselJ(mu + nu + alpha, z)`	`Integrate[BesselJ[\[Mu], z(Sin[\[Theta]])^(2)]BesselJ[\[Nu], z(Cos[\[Theta]])^(2)](Sin[\[Theta]])^(2\[Alpha]- 1) Sec[\[Theta]], {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu]+ \[Alpha]) Gamma[\[Mu]+ \[Alpha]](2)^(\[Alpha]- 1),\[Nu]Gamma[\[Mu]+ 1](z)^\[Alpha]]BesselJ[\[Mu]+ \[Nu]+ \[Alpha], z]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.22.E24	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}\cot@@{\theta}\diff{\theta} = \tfrac{1}{2}\mu^{-1}\BesselJ{\mu+\nu}@{z}}	`int(BesselJ(mu, z(sin(theta))^(2))BesselJ(nu, z(cos(theta))^(2))cot(theta), theta = 0..(1)/(2)Pi) = (1)/(2)(mu)^(- 1)* BesselJ(mu + nu, z)`	`Integrate[BesselJ[\[Mu], z(Sin[\[Theta]])^(2)]BesselJ[\[Nu], z(Cos[\[Theta]])^(2)]Cot[\[Theta]], {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[1,2]\[Mu]^(- 1)* BesselJ[\[Mu]+ \[Nu], z]`	Failure	Aborted	Skipped - Because timed out	Skip - No test values generated
10.22.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\modBesselI{\nu}@{z\cos@@{\theta}}(\tan@@{\theta})^{\mu+1}\diff{\theta} = \frac{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu}(\tfrac{1}{2}z)^{\mu}}{2\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1}}\BesselJ{\nu}@{z}}	`int(BesselJ(mu, zsin(theta))BesselI(nu, zcos(theta))(tan(theta))^(mu + 1), theta = 0..(1)/(2)Pi) = (GAMMA((1)/(2)nu -(1)/(2)mu)((1)/(2)z)^(mu))/(2GAMMA((1)/(2)nu +(1)/(2)mu + 1))*BesselJ(nu, z)`	`Integrate[BesselJ[\[Mu], zSin[\[Theta]]]BesselI[\[Nu], zCos[\[Theta]]](Tan[\[Theta]])^(\[Mu]+ 1), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]\[Nu]-Divide[1,2]\[Mu]](Divide[1,2]z)^\[Mu],2Gamma[Divide[1,2]\[Nu]+Divide[1,2]\[Mu]+ 1]]*BesselJ[\[Nu], z]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.22.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\BesselJ{\nu}@{\zeta\cos@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{\nu+1}\diff{\theta} = \frac{z^{\mu}\zeta^{\nu}\BesselJ{\mu+\nu+1}@{\sqrt{\zeta^{2}+z^{2}}}}{(\zeta^{2}+z^{2})^{\frac{1}{2}(\mu+\nu+1)}}}	`int(BesselJ(mu, zsin(theta))BesselJ(nu, zetacos(theta))(sin(theta))^(mu + 1)(cos(theta))^(nu + 1), theta = 0..(1)/(2)Pi) = ((z)^(mu)* (zeta)^(nu)* BesselJ(mu + nu + 1, sqrt((zeta)^(2)+ (z)^(2))))/(((zeta)^(2)+ (z)^(2))^((1)/(2)*(mu + nu + 1)))`	`Integrate[BesselJ[\[Mu], zSin[\[Theta]]]BesselJ[\[Nu], \[Zeta]Cos[\[Theta]]](Sin[\[Theta]])^(\[Mu]+ 1)(Cos[\[Theta]])^(\[Nu]+ 1), {\[Theta], 0, Divide[1,2]Pi}, GenerateConditions->None] == Divide[(z)^\[Mu]* \[Zeta]^\[Nu]* BesselJ[\[Mu]+ \[Nu]+ 1, Sqrt[\[Zeta]^(2)+ (z)^(2)]],(\[Zeta]^(2)+ (z)^(2))^(Divide[1,2]*(\[Mu]+ \[Nu]+ 1))]`	Error	Aborted	-	Skipped - Because timed out
10.22.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\BesselJ{\nu-1}^{2}@{t}\diff{t} = 2\sum_{k=0}^{\infty}(\nu+2k)\BesselJ{\nu+2k}^{2}@{x}}	`int(t(BesselJ(nu - 1, t))^(2), t = 0..x) = 2sum((nu + 2k) (BesselJ(nu + 2*k, x))^(2), k = 0..infinity)`	`Integrate[t(BesselJ[\[Nu]- 1, t])^(2), {t, 0, x}, GenerateConditions->None] == 2Sum[(\[Nu]+ 2k) (BesselJ[\[Nu]+ 2*k, x])^(2), {k, 0, Infinity}, GenerateConditions->None]`	Failure	Successful	Successful [Tested: 15]	Successful [Tested: 15]
10.22.E28	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\left(\BesselJ{\nu-1}^{2}@{t}-\BesselJ{\nu+1}^{2}@{t}\right)\diff{t} = 2\nu\BesselJ{\nu}^{2}@{x}}	`int(t((BesselJ(nu - 1, t))^(2)- (BesselJ(nu + 1, t))^(2)), t = 0..x) = 2nu*(BesselJ(nu, x))^(2)`	`Integrate[t((BesselJ[\[Nu]- 1, t])^(2)- (BesselJ[\[Nu]+ 1, t])^(2)), {t, 0, x}, GenerateConditions->None] == 2\[Nu]*(BesselJ[\[Nu], x])^(2)`	Successful	Successful	-	Successful [Tested: 15]
10.22.E29	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t\BesselJ{0}^{2}@{t}\diff{t} = \tfrac{1}{2}x^{2}\left(\BesselJ{0}^{2}@{x}+\BesselJ{1}^{2}@{x}\right)}	`int(t(BesselJ(0, t))^(2), t = 0..x) = (1)/(2)(x)^(2)*((BesselJ(0, x))^(2)+ (BesselJ(1, x))^(2))`	`Integrate[t(BesselJ[0, t])^(2), {t, 0, x}, GenerateConditions->None] == Divide[1,2](x)^(2)*((BesselJ[0, x])^(2)+ (BesselJ[1, x])^(2))`	Successful	Successful	-	Successful [Tested: 3]
10.22.E30	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{n}@{t}\BesselJ{n+1}@{t}\diff{t} = \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x}}	`int(BesselJ(n, t)BesselJ(n + 1, t), t = 0..x) = (1)/(2)(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n)`	`Integrate[BesselJ[n, t]BesselJ[n + 1, t], {t, 0, x}, GenerateConditions->None] == Divide[1,2](1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 3]	Failed [2 / 3] {Plus[-0.6308420033135872, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]], {Rule[n, 3], Rule[x, 1.5]} `Plus[-0.9403627636501156, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[0.5, 2], []], Times[Plus[-`
10.22.E30	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x} = \sum_{k=n+1}^{\infty}\BesselJ{k}^{2}@{x}}	`(1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n) = sum((BesselJ(k, x))^(2), k = n + 1..infinity)`	`Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None] == Sum[(BesselJ[k, x])^(2), {k, n + 1, Infinity}, GenerateConditions->None]`	Failure	Failure	Successful [Tested: 3]	Failed [3 / 3] {Plus[0.6309837827773054, Times[-1.0, NSum[Power[BesselJ[k, 1.5], 2] <- {k, 4, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]]], {Rule[n, 3], Rule[x, 1.5]} `Plus[`
10.22.E31	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{\mu+\nu+2k+1}@{x}}	`int(BesselJ(mu, t)BesselJ(nu, x - t), t = 0..x) = 2sum((- 1)^(k)* BesselJ(mu + nu + 2*k + 1, x), k = 0..infinity)`	`Integrate[BesselJ[\[Mu], t]BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == 2Sum[(- 1)^(k)* BesselJ[\[Mu]+ \[Nu]+ 2*k + 1, x], {k, 0, Infinity}, GenerateConditions->None]`	Error	Failure	-	Skip - No test values generated
10.22.E32	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{1-\nu}@{x-t}\diff{t} = \BesselJ{0}@{x}-\cos@@{x}}	`int(BesselJ(nu, t)*BesselJ(1 - nu, x - t), t = 0..x) = BesselJ(0, x)- cos(x)`	`Integrate[BesselJ[\[Nu], t]*BesselJ[1 - \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == BesselJ[0, x]- Cos[x]`	Failure	Failure	Manual Skip!	Skipped - Because timed out
10.22.E33	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{-\nu}@{x-t}\diff{t} = \sin@@{x}}	`int(BesselJ(nu, t)*BesselJ(- nu, x - t), t = 0..x) = sin(x)`	`Integrate[BesselJ[\[Nu], t]*BesselJ[- \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Sin[x]`	Failure	Failure	Manual Skip!	Skipped - Because timed out
10.22.E34	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}t^{-1}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = \frac{\BesselJ{\mu+\nu}@{x}}{\mu}}	`int((t)^(- 1)* BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x) = (BesselJ(mu + nu, x))/(mu)`	`Integrate[(t)^(- 1)* BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Divide[BesselJ[\[Mu]+ \[Nu], x],\[Mu]]`	Failure	Failure	Manual Skip!	Skip - No test values generated
10.22.E35	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t}}{t(x-t)} = \frac{(\mu+\nu)\BesselJ{\mu+\nu}@{x}}{\mu\nu x}}	`int((BesselJ(mu, t)BesselJ(nu, x - t))/(t(x - t)), t = 0..x) = ((mu + nu)* BesselJ(mu + nu, x))/(munux)`	`Integrate[Divide[BesselJ[\[Mu], t]BesselJ[\[Nu], x - t],t(x - t)], {t, 0, x}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu])* BesselJ[\[Mu]+ \[Nu], x],\[Mu]\[Nu]x]`	Error	Failure	-	Skip - No test values generated
10.22.E36	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{\alpha}}\int_{0}^{x}(x-t)^{\alpha-1}\BesselJ{\nu}@{t}\diff{t} = 2^{\alpha}\sum_{k=0}^{\infty}\frac{(\alpha)_{k}}{k!}\BesselJ{\nu+\alpha+2k}@{x}}	`(1)/(GAMMA(alpha))int((x - t)^(alpha - 1) BesselJ(nu, t), t = 0..x) = (2)^(alpha)* sum((alpha[k])/(factorial(k))BesselJ(nu + alpha + 2k, x), k = 0..infinity)`	`Divide[1,Gamma[\[Alpha]]]Integrate[(x - t)^(\[Alpha]- 1) BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == (2)^\[Alpha]* Sum[Divide[Subscript[\[Alpha], k],(k)!]BesselJ[\[Nu]+ \[Alpha]+ 2k, x], {k, 0, Infinity}, GenerateConditions->None]`	Error	Failure	-	Skip - No test values generated
10.22.E37	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t\BesselJ{\nu}@{j_{\nu,\ell}t}\BesselJ{\nu}@{j_{\nu,m}t}\diff{t} = \tfrac{1}{2}\left(\BesselJ{\nu}'@{j_{\nu,\ell}}\right)^{2}\Kroneckerdelta{\ell}{m}}	`int(tBesselJ(nu, j[nu , ell]t)BesselJ(nu, j[nu , m]t), t = 0..1) = (1)/(2)(diff( BesselJ(nu, j[nu , ell]), j[nu , ell]$(1) ))^(2) KroneckerDelta[ell, m]`	`Integrate[tBesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]t]BesselJ[\[Nu], Subscript[j, \[Nu], m]t], {t, 0, 1}, GenerateConditions->None] == Divide[1,2](D[BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]], {Subscript[j, \[Nu], \[ScriptL]], 1}])^(2) KroneckerDelta[\[ScriptL], m]`	Failure	Failure	Error	Failed [300 / 300] `{Indeterminate <- {Rule[m, 1], Rule[ℓ, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Indeterminate <- {Rule[m, 1], Rule[ℓ, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.22.E38	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t\BesselJ{\nu}@{\alpha_{\ell}t}\BesselJ{\nu}@{\alpha_{m}t}\diff{t} = \left(\frac{a^{2}}{b^{2}}+\alpha_{\ell}^{2}-\nu^{2}\right)\frac{(\BesselJ{\nu}@{\alpha_{\ell}})^{2}}{2\alpha_{\ell}^{2}}\Kroneckerdelta{\ell}{m}}	`int(tBesselJ(nu, alpha[ell]t)BesselJ(nu, alpha[m]t), t = 0..1) ((BesselJ(nu, alpha[ell]))^(2))/(2alpha(alpha[ell])^(2))KroneckerDelta[ell, m]`	`Integrate[tBesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]t]BesselJ[\[Nu], Subscript[\[Alpha], m]t], {t, 0, 1}, GenerateConditions->None] Divide[(BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]])^(2),2\[Alpha](Subscript[\[Alpha], \[ScriptL]])^(2)]KroneckerDelta[\[ScriptL], m]`	Failure	Failure	Error	Failed [300 / 300] `{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[m, 1], Rule[α, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[m, 2], Rule[α, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.22.E39	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\BesselJ{0}@{t}}{t}\diff{t}+\EulerConstant+\ln@{\tfrac{1}{2}x} = \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t}}	`int((BesselJ(0, t))/(t), t = x..infinity)+ gamma + ln((1)/(2)*x) = int((1 - BesselJ(0, t))/(t), t = 0..x)`	`Integrate[Divide[BesselJ[0, t],t], {t, x, Infinity}, GenerateConditions->None]+ EulerGamma + Log[Divide[1,2]*x] == Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 3]
10.22.E39	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \sum_{k=1}^{\infty}(-1)^{k-1}\frac{(\frac{1}{2}x)^{2k}}{2k(k!)^{2}}}	`int((1 - BesselJ(0, t))/(t), t = 0..x) = sum((- 1)^(k - 1)(((1)/(2)x)^(2k))/(2k*(factorial(k))^(2)), k = 1..infinity)`	`Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Sum[(- 1)^(k - 1)Divide[(Divide[1,2]x)^(2k),2k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 3]
10.22.E40	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\BesselY{0}@{t}}{t}\diff{t} = -\frac{1}{\pi}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi}{6}+\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\*\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}}	`int((BesselY(0, t))/(t), t = x..infinity) = -(1)/(Pi)(ln((1)/(2)x)+ gamma)^(2)+(Pi)/(6)+(2)/(Pi)sum((- 1)^(k)(Psi(k + 1)+(1)/(2k)- ln((1)/(2)x))(((1)/(2)x)^(2k))/(2k*(factorial(k))^(2)), k = 1..infinity)`	`Integrate[Divide[BesselY[0, t],t], {t, x, Infinity}, GenerateConditions->None] == -Divide[1,Pi](Log[Divide[1,2]x]+ EulerGamma)^(2)+Divide[Pi,6]+Divide[2,Pi]Sum[(- 1)^(k)(PolyGamma[k + 1]+Divide[1,2k]- Log[Divide[1,2]x])Divide[(Divide[1,2]x)^(2k),2k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]`	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.22.E41	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{t}\diff{t} = 1}	`int(BesselJ(nu, t), t = 0..infinity) = 1`	`Integrate[BesselJ[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == 1`	Successful	Successful	-	Successful [Tested: 8]
10.22.E42	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{\nu}@{t}\diff{t} = -\tan@{\tfrac{1}{2}\nu\pi}}	`int(BesselY(nu, t), t = 0..infinity) = - tan((1)/(2)nuPi)`	`Integrate[BesselY[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == - Tan[Divide[1,2]\[Nu]Pi]`	Successful	Aborted	-	Successful [Tested: 6]
10.22.E43	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = 2^{\mu}\frac{\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+\tfrac{1}{2}}}}	`int((t)^(mu)* BesselJ(nu, t), t = 0..infinity) = (2)^(mu)(GAMMA((1)/(2)nu +(1)/(2)mu +(1)/(2)))/(GAMMA((1)/(2)nu -(1)/(2)*mu +(1)/(2)))`	`Integrate[(t)^\[Mu]* BesselJ[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == (2)^\[Mu]Divide[Gamma[Divide[1,2]\[Nu]+Divide[1,2]\[Mu]+Divide[1,2]],Gamma[Divide[1,2]\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]]`	Successful	Successful	-	Successful [Tested: 10]
10.22.E44	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu}\BesselY{\nu}@{t}\diff{t} = \frac{2^{\mu}}{\pi}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}}\sin@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\pi}	`int((t)^(mu)* BesselY(nu, t), t = 0..infinity) = ((2)^(mu))/(Pi)GAMMA((1)/(2)mu +(1)/(2)nu +(1)/(2))GAMMA((1)/(2)mu -(1)/(2)nu +(1)/(2))sin((1)/(2)mu -(1)/(2)nu)Pi`	`Integrate[(t)^\[Mu]* BesselY[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[(2)^\[Mu],Pi]Gamma[Divide[1,2]\[Mu]+Divide[1,2]\[Nu]+Divide[1,2]]Gamma[Divide[1,2]\[Mu]-Divide[1,2]\[Nu]+Divide[1,2]]Sin[Divide[1,2]\[Mu]-Divide[1,2]\[Nu]]Pi`	Error	Aborted	-	Failed [10 / 10] `{Complex[-0.5512405929316078, 0.2551977660147906] <- {Rule[μ, 0], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.26217720344291356, -0.18052742798771904] <- {Rule[μ, 0], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.22.E45	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{1-\BesselJ{0}@{t}}{t^{\mu}}\diff{t} = -\frac{\pi\sec@{\frac{1}{2}\mu\pi}}{2^{\mu}\EulerGamma^{2}@{\frac{1}{2}\mu+\frac{1}{2}}}}	`int((1 - BesselJ(0, t))/((t)^(mu)), t = 0..infinity) = -(Pisec((1)/(2)muPi))/((2)^(mu) (GAMMA((1)/(2)*mu +(1)/(2)))^(2))`	`Integrate[Divide[1 - BesselJ[0, t],(t)^\[Mu]], {t, 0, Infinity}, GenerateConditions->None] == -Divide[PiSec[Divide[1,2]\[Mu]Pi],(2)^\[Mu] (Gamma[Divide[1,2]*\[Mu]+Divide[1,2]])^(2)]`	Error	Aborted	-	Successful [Tested: 10]
10.22.E46	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{t^{\nu+1}\BesselJ{\nu}@{at}}{(t^{2}+b^{2})^{\mu+1}}\diff{t} = \frac{a^{\mu}b^{\nu-\mu}}{2^{\mu}\EulerGamma@{\mu+1}}\modBesselK{\nu-\mu}@{ab}}	`int(((t)^(nu + 1)* BesselJ(nu, at))/(((t)^(2)+ (b)^(2))^(mu + 1)), t = 0..infinity) = ((a)^(mu) (b)^(nu - mu))/((2)^(mu)* GAMMA(mu + 1))BesselK(nu - mu, ab)`	`Integrate[Divide[(t)^(\[Nu]+ 1)* BesselJ[\[Nu], at],((t)^(2)+ (b)^(2))^(\[Mu]+ 1)], {t, 0, Infinity}, GenerateConditions->None] == Divide[(a)^\[Mu] (b)^(\[Nu]- \[Mu]),(2)^\[Mu]* Gamma[\[Mu]+ 1]]BesselK[\[Nu]- \[Mu], ab]`	Error	Aborted	-	Skipped - Because timed out
10.22.E47	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{t^{\nu}\BesselY{\nu}@{at}}{t^{2}+b^{2}}\diff{t} = -b^{\nu-1}\modBesselK{\nu}@{ab}}	`int(((t)^(nu)* BesselY(nu, at))/((t)^(2)+ (b)^(2)), t = 0..infinity) = - (b)^(nu - 1) BesselK(nu, a*b)`	`Integrate[Divide[(t)^\[Nu]* BesselY[\[Nu], at],(t)^(2)+ (b)^(2)], {t, 0, Infinity}, GenerateConditions->None] == - (b)^(\[Nu]- 1) BesselK[\[Nu], a*b]`	Error	Aborted	-	Skipped - Because timed out
10.22.E48	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{x\cosh@@{\phi}}(\cosh@@{\phi})^{1-\mu}(\sinh@@{\phi})^{2\nu+1}\diff{\phi} = 2^{\nu}\EulerGamma@{\nu+1}x^{-\nu-1}\BesselJ{\mu-\nu-1}@{x}}	`int(BesselJ(mu, xcosh(phi))(cosh(phi))^(1 - mu)(sinh(phi))^(2nu + 1), phi = 0..infinity) = (2)^(nu)* GAMMA(nu + 1)(x)^(- nu - 1) BesselJ(mu - nu - 1, x)`	`Integrate[BesselJ[\[Mu], xCosh[\[Phi]]](Cosh[\[Phi]])^(1 - \[Mu])(Sinh[\[Phi]])^(2\[Nu]+ 1), {\[Phi], 0, Infinity}, GenerateConditions->None] == (2)^\[Nu]* Gamma[\[Nu]+ 1](x)^(- \[Nu]- 1) BesselJ[\[Mu]- \[Nu]- 1, x]`	Error	Aborted	-	Skipped - Because timed out
10.22.E49	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}e^{-at}\BesselJ{\nu}@{bt}\diff{t} = \frac{(\tfrac{1}{2}b)^{\nu}}{a^{\mu+\nu}}\EulerGamma@{\mu+\nu}\*\hyperOlverF@{\frac{\mu+\nu}{2}}{\frac{\mu+\nu+1}{2}}{\nu+1}{-\frac{b^{2}}{a^{2}}}}	`int((t)^(mu - 1)* exp(- at)BesselJ(nu, bt), t = 0..infinity) = (((1)/(2)b)^(nu))/((a)^(mu + nu))GAMMA(mu + nu) hypergeom([(mu + nu)/(2), (mu + nu + 1)/(2)], [nu + 1], -((b)^(2))/((a)^(2)))/GAMMA(nu + 1)`	`Integrate[(t)^(\[Mu]- 1)* Exp[- at]BesselJ[\[Nu], bt], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Divide[1,2]b)^\[Nu],(a)^(\[Mu]+ \[Nu])]Gamma[\[Mu]+ \[Nu]] Hypergeometric2F1Regularized[Divide[\[Mu]+ \[Nu],2], Divide[\[Mu]+ \[Nu]+ 1,2], \[Nu]+ 1, -Divide[(b)^(2),(a)^(2)]]`	Error	Aborted	-	Successful [Tested: 0]
10.22.E50	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}e^{-at}\BesselY{\nu}@{bt}\diff{t} = \cot@{\nu\pi}\frac{(\tfrac{1}{2}b)^{\nu}\EulerGamma@{\mu+\nu}}{(a^{2}+b^{2})^{\frac{1}{2}(\mu+\nu)}}\\hyperOlverF@{\frac{\mu+\nu}{2}}{\frac{1-\mu+\nu}{2}}{\nu+1}{\frac{b^{2}}{a^{2}+b^{2}}}-\csc@{\nu\pi}\frac{(\tfrac{1}{2}b)^{-\nu}\EulerGamma@{\mu-\nu}}{(a^{2}+b^{2})^{\frac{1}{2}(\mu-\nu)}}\\hyperOlverF@{\frac{\mu-\nu}{2}}{\frac{1-\mu-\nu}{2}}{1-\nu}{\frac{b^{2}}{a^{2}+b^{2}}}}	`int((t)^(mu - 1)* exp(- at)BesselY(nu, bt), t = 0..infinity) = cot(nuPi)(((1)/(2)b)^(nu)* GAMMA(mu + nu))/(((a)^(2)+ (b)^(2))^((1)/(2)(mu + nu))) hypergeom([(mu + nu)/(2), (1 - mu + nu)/(2)], [nu + 1], ((b)^(2))/((a)^(2)+ (b)^(2)))/GAMMA(nu + 1)- csc(nuPi)(((1)/(2)b)^(- nu) GAMMA(mu - nu))/(((a)^(2)+ (b)^(2))^((1)/(2)(mu - nu))) hypergeom([(mu - nu)/(2), (1 - mu - nu)/(2)], [1 - nu], ((b)^(2))/((a)^(2)+ (b)^(2)))/GAMMA(1 - nu)`	Integrate[(t)^(\[Mu]- 1)* Exp[- at]BesselY[\[Nu], bt], {t, 0, Infinity}, GenerateConditions->None] == Cot[\[Nu]Pi]Divide[(Divide[1,2]b)^\[Nu]* Gamma[\[Mu]+ \[Nu]],((a)^(2)+ (b)^(2))^(Divide[1,2](\[Mu]+ \[Nu]))] Hypergeometric2F1Regularized[Divide[\[Mu]+ \[Nu],2], Divide[1 - \[Mu]+ \[Nu],2], \[Nu]+ 1, Divide[(b)^(2),(a)^(2)+ (b)^(2)]]- Csc[\[Nu]Pi]Divide[(Divide[1,2]b)^(- \[Nu]) Gamma[\[Mu]- \[Nu]],((a)^(2)+ (b)^(2))^(Divide[1,2](\[Mu]- \[Nu]))] Hypergeometric2F1Regularized[Divide[\[Mu]- \[Nu],2], Divide[1 - \[Mu]- \[Nu],2], 1 - \[Nu], Divide[(b)^(2),(a)^(2)+ (b)^(2)]]	Error	Aborted	-	Skipped - Because timed out
10.22.E51	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}t^{\nu+1}\diff{t} = \frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp@{-\frac{b^{2}}{4p^{2}}}}	`int(BesselJ(nu, bt)exp(- (p)^(2)* (t)^(2))(t)^(nu + 1), t = 0..infinity) = ((b)^(nu))/((2(p)^(2))^(nu + 1))exp(-((b)^(2))/(4(p)^(2)))`	`Integrate[BesselJ[\[Nu], bt]Exp[- (p)^(2)* (t)^(2)](t)^(\[Nu]+ 1), {t, 0, Infinity}, GenerateConditions->None] == Divide[(b)^\[Nu],(2(p)^(2))^(\[Nu]+ 1)]Exp[-Divide[(b)^(2),4(p)^(2)]]`	Error	Aborted	-	Failed [151 / 300] `{Complex[-0.06577510728447342, -0.5886826409090221] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.0556301041786353, -0.2359104145157832] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.22.E52	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{-\frac{b^{2}}{8p^{2}}}\modBesselI{\ifrac{\nu}{2}}@{\frac{b^{2}}{8p^{2}}}}	`int(BesselJ(nu, bt)exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(2p)exp(-((b)^(2))/(8(p)^(2)))BesselI((nu)/(2), ((b)^(2))/(8*(p)^(2)))`	`Integrate[BesselJ[\[Nu], bt]Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],2p]Exp[-Divide[(b)^(2),8(p)^(2)]]BesselI[Divide[\[Nu],2], Divide[(b)^(2),8*(p)^(2)]]`	Error	Aborted	-	Skip - No test values generated
10.22.E53	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{2\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = -\frac{\sqrt{\pi}}{2p}\exp@{-\frac{b^{2}}{8p^{2}}}\left(\modBesselI{\nu}@{\frac{b^{2}}{8p^{2}}}\tan@{\nu\pi}+\frac{1}{\pi}\modBesselK{\nu}@{\frac{b^{2}}{8p^{2}}}\sec@{\nu\pi}\right)}	`int(BesselY(2nu, bt)exp(- (p)^(2) (t)^(2)), t = 0..infinity) = -(sqrt(Pi))/(2p)exp(-((b)^(2))/(8(p)^(2)))(BesselI(nu, ((b)^(2))/(8(p)^(2)))tan(nuPi)+(1)/(Pi)BesselK(nu, ((b)^(2))/(8(p)^(2)))sec(nu*Pi))`	`Integrate[BesselY[2\[Nu], bt]Exp[- (p)^(2) (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == -Divide[Sqrt[Pi],2p]Exp[-Divide[(b)^(2),8(p)^(2)]](BesselI[\[Nu], Divide[(b)^(2),8(p)^(2)]]Tan[\[Nu]Pi]+Divide[1,Pi]BesselK[\[Nu], Divide[(b)^(2),8(p)^(2)]]Sec[\[Nu]*Pi])`	Error	Aborted	-	Skipped - Because timed out
10.22.E54	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}t^{\mu-1}\diff{t} = \frac{(\tfrac{1}{2}b/p)^{\nu}\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu}}{2p^{\mu}}\exp@{-\frac{b^{2}}{4p^{2}}}\*\OlverconfhyperM@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+1}{\nu+1}{\frac{b^{2}}{4p^{2}}}}	`int(BesselJ(nu, bt)exp(- (p)^(2)* (t)^(2))(t)^(mu - 1), t = 0..infinity) = (((1)/(2)b/ p)^(nu)* GAMMA((1)/(2)nu +(1)/(2)mu))/(2(p)^(mu))exp(-((b)^(2))/(4(p)^(2))) KummerM((1)/(2)nu -(1)/(2)mu + 1, nu + 1, ((b)^(2))/(4*(p)^(2)))/GAMMA(nu + 1)`	`Integrate[BesselJ[\[Nu], bt]Exp[- (p)^(2)* (t)^(2)](t)^(\[Mu]- 1), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Divide[1,2]b/ p)^\[Nu]* Gamma[Divide[1,2]\[Nu]+Divide[1,2]\[Mu]],2(p)^\[Mu]]Exp[-Divide[(b)^(2),4(p)^(2)]] Hypergeometric1F1Regularized[Divide[1,2]\[Nu]-Divide[1,2]\[Mu]+ 1, \[Nu]+ 1, Divide[(b)^(2),4*(p)^(2)]]`	Error	Aborted	-	Failed [246 / 300] `{Complex[0.07541885663346475, -0.6281916024632631] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.1002850405400357, -0.7734416454563844] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.22.E55	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{-1}\BesselJ{\nu+2\ell+1}@{t}\BesselJ{\nu+2m+1}@{t}\diff{t} = \frac{\Kroneckerdelta{\ell}{m}}{2(2\ell+\nu+1)}}	`int((t)^(- 1)* BesselJ(nu + 2ell + 1, t)BesselJ(nu + 2m + 1, t), t = 0..infinity) = (KroneckerDelta[ell, m])/(2(2*ell + nu + 1))`	`Integrate[(t)^(- 1)* BesselJ[\[Nu]+ 2\[ScriptL]+ 1, t]BesselJ[\[Nu]+ 2m + 1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[KroneckerDelta[\[ScriptL], m],2(2*\[ScriptL]+ \[Nu]+ 1)]`	Failure	Failure	Error	Failed [18 / 54] `{Indeterminate <- {Rule[m, 1], Rule[ℓ, 1], Rule[ν, Rational[-3, 2]]}` `Indeterminate <- {Rule[m, 2], Rule[ℓ, 2], Rule[ν, Rational[-3, 2]]}`
10.22.E56	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{a^{\mu}\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu-\frac{1}{2}\lambda+\frac{1}{2}}}{2^{\lambda}b^{\mu-\lambda+1}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\lambda+\frac{1}{2}}}\*\hyperOlverF@{\tfrac{1}{2}(\mu+\nu-\lambda+1)}{\tfrac{1}{2}(\mu-\nu-\lambda+1)}{\mu+1}{\frac{a^{2}}{b^{2}}}}	`int((BesselJ(mu, at)BesselJ(nu, bt))/((t)^(lambda)), t = 0..infinity) = ((a)^(mu) GAMMA((1)/(2)nu +(1)/(2)mu -(1)/(2)lambda +(1)/(2)))/((2)^(lambda) (b)^(mu - lambda + 1)* GAMMA((1)/(2)nu -(1)/(2)mu +(1)/(2)lambda +(1)/(2))) hypergeom([(1)/(2)(mu + nu - lambda + 1), (1)/(2)(mu - nu - lambda + 1)], [mu + 1], ((a)^(2))/((b)^(2)))/GAMMA(mu + 1)`	`Integrate[Divide[BesselJ[\[Mu], at]BesselJ[\[Nu], bt],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(a)^\[Mu] Gamma[Divide[1,2]\[Nu]+Divide[1,2]\[Mu]-Divide[1,2]\[Lambda]+Divide[1,2]],(2)^\[Lambda] (b)^(\[Mu]- \[Lambda]+ 1)* Gamma[Divide[1,2]\[Nu]-Divide[1,2]\[Mu]+Divide[1,2]\[Lambda]+Divide[1,2]]] Hypergeometric2F1Regularized[Divide[1,2](\[Mu]+ \[Nu]- \[Lambda]+ 1), Divide[1,2](\[Mu]- \[Nu]- \[Lambda]+ 1), \[Mu]+ 1, Divide[(a)^(2),(b)^(2)]]`	Error	Aborted	-	Failed [300 / 300] `{Complex[0.12507202091813296, -0.11002587193353452] <- {Rule[a, 1.5], Rule[b, 2], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.017959797138118128, 0.3252875517547388] <- {Rule[a, 1.5], Rule[b, 2], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.22.E57	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\BesselJ{\mu}@{at}\BesselJ{\nu}@{at}}{t^{\lambda}}\diff{t} = \frac{(\frac{1}{2}a)^{\lambda-1}\EulerGamma@{\frac{1}{2}\mu+\frac{1}{2}\nu-\frac{1}{2}\lambda+\frac{1}{2}}\EulerGamma@{\lambda}}{2\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\mu-\frac{1}{2}\nu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}\nu+\frac{1}{2}}}}	`int((BesselJ(mu, at)BesselJ(nu, at))/((t)^(lambda)), t = 0..infinity) = (((1)/(2)a)^(lambda - 1)* GAMMA((1)/(2)mu +(1)/(2)nu -(1)/(2)lambda +(1)/(2))GAMMA(lambda))/(2GAMMA((1)/(2)lambda +(1)/(2)nu -(1)/(2)mu +(1)/(2))GAMMA((1)/(2)lambda +(1)/(2)mu -(1)/(2)nu +(1)/(2))GAMMA((1)/(2)lambda +(1)/(2)mu +(1)/(2)nu +(1)/(2)))`	`Integrate[Divide[BesselJ[\[Mu], at]BesselJ[\[Nu], at],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Divide[1,2]a)^(\[Lambda]- 1)* Gamma[Divide[1,2]\[Mu]+Divide[1,2]\[Nu]-Divide[1,2]\[Lambda]+Divide[1,2]]Gamma[\[Lambda]],2Gamma[Divide[1,2]\[Lambda]+Divide[1,2]\[Nu]-Divide[1,2]\[Mu]+Divide[1,2]]Gamma[Divide[1,2]\[Lambda]+Divide[1,2]\[Mu]-Divide[1,2]\[Nu]+Divide[1,2]]Gamma[Divide[1,2]\[Lambda]+Divide[1,2]\[Mu]+Divide[1,2]\[Nu]+Divide[1,2]]]`	Error	Aborted	-	Skipped - Because timed out
10.22.E58	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\BesselJ{\nu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{(ab)^{\nu}\EulerGamma@{\nu-\frac{1}{2}\lambda+\frac{1}{2}}}{2^{\lambda}(a^{2}+b^{2})^{\nu-\frac{1}{2}\lambda+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}}}\hyperOlverF@{\frac{2\nu+1-\lambda}{4}}{\frac{2\nu+3-\lambda}{4}}{\nu+1}{\frac{4a^{2}b^{2}}{(a^{2}+b^{2})^{2}}}}	`int((BesselJ(nu, at)BesselJ(nu, bt))/((t)^(lambda)), t = 0..infinity) = ((ab)^(nu)* GAMMA(nu -(1)/(2)lambda +(1)/(2)))/((2)^(lambda)((a)^(2)+ (b)^(2))^(nu -(1)/(2)lambda +(1)/(2)) GAMMA((1)/(2)lambda +(1)/(2)))hypergeom([(2nu + 1 - lambda)/(4), (2nu + 3 - lambda)/(4)], [nu + 1], (4(a)^(2) (b)^(2))/(((a)^(2)+ (b)^(2))^(2)))/GAMMA(nu + 1)`	`Integrate[Divide[BesselJ[\[Nu], at]BesselJ[\[Nu], bt],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(ab)^\[Nu]* Gamma[\[Nu]-Divide[1,2]\[Lambda]+Divide[1,2]],(2)^\[Lambda]((a)^(2)+ (b)^(2))^(\[Nu]-Divide[1,2]\[Lambda]+Divide[1,2]) Gamma[Divide[1,2]\[Lambda]+Divide[1,2]]]Hypergeometric2F1Regularized[Divide[2\[Nu]+ 1 - \[Lambda],4], Divide[2\[Nu]+ 3 - \[Lambda],4], \[Nu]+ 1, Divide[4(a)^(2) (b)^(2),((a)^(2)+ (b)^(2))^(2)]]`	Error	Aborted	-	Failed [209 / 300] `{Complex[-0.13393539357334844, 0.1322614378889556] <- {Rule[a, -1.5], Rule[b, -0.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.07230690300251369, -0.15068591568973605] <- {Rule[a, -1.5], Rule[b, -0.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}`
10.22.E66	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}\diff{t} = \frac{1}{\pi(bc)^{\frac{1}{2}}}\*\assLegendreQ[]{\nu-\frac{1}{2}}@{\frac{a^{2}+b^{2}+c^{2}}{2bc}}}	`int(exp(- at)BesselJ(nu, bt)BesselJ(nu, ct), t = 0..infinity) = (1)/(Pi(bc)^((1)/(2))) LegendreQ(nu -(1)/(2), ((a)^(2)+ (b)^(2)+ (c)^(2))/(2bc))`	`Integrate[Exp[- at]BesselJ[\[Nu], bt]BesselJ[\[Nu], ct], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,Pi(bc)^(Divide[1,2])] LegendreQ[\[Nu]-Divide[1,2], 0, 3, Divide[(a)^(2)+ (b)^(2)+ (c)^(2),2bc]]`	Error	Aborted	-	Skipped - Because timed out
10.22.E67	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\BesselJ{\nu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \frac{1}{2p^{2}}\exp@{-\frac{a^{2}+b^{2}}{4p^{2}}}\modBesselI{\nu}\left(\frac{ab}{2p^{2}}\right)}	`int(texp(- (p)^(2) (t)^(2))BesselJ(nu, at)BesselJ(nu, bt), t = 0..infinity) = (1)/(2(p)^(2))exp(-((a)^(2)+ (b)^(2))/(4(p)^(2)))BesselI(nu, (ab)/(2(p)^(2)))`	`Integrate[tExp[- (p)^(2) (t)^(2)]BesselJ[\[Nu], at]BesselJ[\[Nu], bt], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2(p)^(2)]Exp[-Divide[(a)^(2)+ (b)^(2),4(p)^(2)]]BesselI[\[Nu], Divide[ab,2(p)^(2)]]`	Translation Error	Translation Error	-	-
10.22.E68	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\BesselJ{0}@{at}\BesselY{0}@{at}\diff{t} = -\frac{1}{2\pi p^{2}}\exp@{-\frac{a^{2}}{2p^{2}}}\modBesselK{0}\left(\frac{a^{2}}{2p^{2}}\right)}	`int(texp(- (p)^(2) (t)^(2))BesselJ(0, at)BesselY(0, at), t = 0..infinity) = -(1)/(2Pi(p)^(2))exp(-((a)^(2))/(2(p)^(2)))BesselK(0, ((a)^(2))/(2(p)^(2)))`	`Integrate[tExp[- (p)^(2) (t)^(2)]BesselJ[0, at]BesselY[0, at], {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,2Pi(p)^(2)]Exp[-Divide[(a)^(2),2(p)^(2)]]BesselK[0, Divide[(a)^(2),2(p)^(2)]]`	Translation Error	Translation Error	-	-
10.22.E70	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselY{\nu}@{at}\BesselJ{\nu+1}@{bt}\frac{t\diff{t}}{t^{2}-z^{2}} = \frac{1}{2}\pi\BesselJ{\nu+1}@{bz}\HankelH{1}{\nu}@{az}}	`int(BesselY(nu, at)BesselJ(nu + 1, bt)(t)/((t)^(2)- (z)^(2)), t = 0..infinity) = (1)/(2)PiBesselJ(nu + 1, bz)HankelH1(nu, a*z)`	`Integrate[BesselY[\[Nu], at]BesselJ[\[Nu]+ 1, bt]Divide[t,(t)^(2)- (z)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]PiBesselJ[\[Nu]+ 1, bz]HankelH1[\[Nu], a*z]`	Error	Aborted	-	Skipped - Because timed out
10.22.E71	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1-\mu}\diff{t} = \frac{(bc)^{\mu-1}(\sin@@{\phi})^{\mu-\frac{1}{2}}}{(2\pi)^{\frac{1}{2}}a^{\mu}}\FerrersP[\frac{1}{2}-\mu]{\nu-\frac{1}{2}}(\cos@@{\phi})}	`int(BesselJ(mu, at)BesselJ(nu, bt)BesselJ(nu, ct)(t)^(1 - mu), t = 0..infinity) = ((bc)^(mu - 1)(sin(phi))^(mu -(1)/(2)))/((2Pi)^((1)/(2)) (a)^(mu))*LegendreP(nu -(1)/(2), (1)/(2)- mu, cos(phi))`	`Integrate[BesselJ[\[Mu], at]BesselJ[\[Nu], bt]BesselJ[\[Nu], ct](t)^(1 - \[Mu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(bc)^(\[Mu]- 1)(Sin[\[Phi]])^(\[Mu]-Divide[1,2]),(2Pi)^(Divide[1,2]) (a)^\[Mu]]*LegendreP[\[Nu]-Divide[1,2], Divide[1,2]- \[Mu], Cos[\[Phi]]]`	Translation Error	Translation Error	-	-
10.22.E72	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1-\mu}\diff{t} = \frac{(bc)^{\mu-1}\sin@{(\mu-\nu)\cpi}(\sinh@@{\chi})^{\mu-\frac{1}{2}}}{(\frac{1}{2}\pi^{3})^{\frac{1}{2}}a^{\mu}}\expe^{(\mu-\frac{1}{2})\iunit\cpi}\assLegendreQ[\frac{1}{2}-\mu]{\nu-\frac{1}{2}}@{\cosh@@{\chi}}}	`int(BesselJ(mu, at)BesselJ(nu, bt)BesselJ(nu, ct)(t)^(1 - mu), t = 0..infinity) = ((bc)^(mu - 1) sin((mu - nu)* Pi)(sinh(chi))^(mu -(1)/(2)))/(((1)/(2)(Pi)^(3))^((1)/(2))* (a)^(mu))exp((mu -(1)/(2)) IPi)LegendreQ(nu -(1)/(2), (1)/(2)- mu, cosh(chi))`	`Integrate[BesselJ[\[Mu], at]BesselJ[\[Nu], bt]BesselJ[\[Nu], ct](t)^(1 - \[Mu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(bc)^(\[Mu]- 1) Sin[(\[Mu]- \[Nu])* Pi](Sinh[\[Chi]])^(\[Mu]-Divide[1,2]),(Divide[1,2](Pi)^(3))^(Divide[1,2])* (a)^\[Mu]]Exp[(\[Mu]-Divide[1,2]) IPi]LegendreQ[\[Nu]-Divide[1,2], Divide[1,2]- \[Mu], 3, Cosh[\[Chi]]]`	Error	Aborted	-	Skip - No test values generated
10.23.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}^{2}@{z}+2\sum_{k=1}^{\infty}\BesselJ{k}^{2}@{z} = 1}	`(BesselJ(0, z))^(2)+ 2*sum((BesselJ(k, z))^(2), k = 1..infinity) = 1`	`(BesselJ[0, z])^(2)+ 2*Sum[(BesselJ[k, z])^(2), {k, 1, Infinity}, GenerateConditions->None] == 1`	Aborted	Successful	Successful [Tested: 7]	Successful [Tested: 7]
10.23.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{2n}(-1)^{k}\BesselJ{k}@{z}\BesselJ{2n-k}@{z}\\ +2\sum_{k=1}^{\infty}\BesselJ{k}@{z}\BesselJ{2n+k}@{z} = 0}	`sum((- 1)^(k)* BesselJ(k, z)BesselJ(2n - k, z), k = 0..2n)+ 2sum(BesselJ(k, z)BesselJ(2n + k, z), k = 1..infinity) = 0`	`Sum[(- 1)^(k)* BesselJ[k, z]BesselJ[2n - k, z], {k, 0, 2n}, GenerateConditions->None]+ 2Sum[BesselJ[k, z]BesselJ[2n + k, z], {k, 1, Infinity}, GenerateConditions->None] == 0`	Error	Failure	-	Failed [21 / 21] `{Plus[Complex[0.00727987412712798, -0.017853077134921347], Times[2.0, NSum[Times[BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[2.4034761502300195^-4, -3.087748713313073^-5], Times[2.0, NSum[Times[BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[4, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.23.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{n}\BesselJ{k}@{z}\BesselJ{n-k}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{k}@{z}\BesselJ{n+k}@{z} = \BesselJ{n}@{2z}}	`sum(BesselJ(k, z)BesselJ(n - k, z), k = 0..n)+ 2sum((- 1)^(k)* BesselJ(k, z)BesselJ(n + k, z), k = 1..infinity) = BesselJ(n, 2z)`	`Sum[BesselJ[k, z]BesselJ[n - k, z], {k, 0, n}, GenerateConditions->None]+ 2Sum[(- 1)^(k)* BesselJ[k, z]BesselJ[n + k, z], {k, 1, Infinity}, GenerateConditions->None] == BesselJ[n, 2z]`	Aborted	Failure	Skipped - Because timed out	Failed [21 / 21] `{Plus[Complex[0.024343533040476317, 0.10797471990649704], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[1, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.006069425709337772, 0.017711723121060452], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.23#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = \sqrt{u^{2}+v^{2}-2uv\cos@@{\alpha}}}	`w = sqrt((u)^(2)+ (v)^(2)- 2uv*cos(alpha))`	`w == Sqrt[(u)^(2)+ (v)^(2)- 2uv*Cos[\[Alpha]]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.3146075610-.1816387601I <- {alpha = 3/2, u = 1/23^(1/2)+1/2I, v = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I}` `-1.680632965+.1843866439I <- {alpha = 3/2, u = 1/23^(1/2)+1/2I, v = 1/23^(1/2)+1/2I, w = -1/2+1/2I3^(1/2)}`	Failed [300 / 300] `{Complex[-0.3146075609842255, -0.18163876002333418] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}` `Complex[0.4375091763619045, 0.252596040745477] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}`
10.23#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u-v\cos@@{\alpha} = w\cos@@{\chi}}	`u - vcos(alpha) = wcos(chi)`	`u - vCos[\[Alpha]] == wCos[\[Chi]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[-.263783978e-1+.4431282844I <- {alpha = 3/2, chi = 1/23^(1/2)+1/2I, u = 1/23^(1/2)+1/2I, v = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I}` `.8262683052-.3665121890I <- {alpha = 3/2, chi = 1/23^(1/2)+1/2I, u = 1/23^(1/2)+1/2I, v = 1/23^(1/2)+1/2I, w = -1/2+1/2I3^(1/2)}`	Failed [300 / 300] `{Complex[-0.026378398027867456, 0.44312828415668515] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.023973249213014358, -0.5554825514041751] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.23#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle v\sin@@{\alpha} = w\sin@@{\chi}}	`vsin(alpha) = wsin(chi)`	`vSin[\[Alpha]] == wSin[\[Chi]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[.2887554391-.2231097873I <- {alpha = 3/2, chi = 1/23^(1/2)+1/2I, v = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I}` `1.585713279-.763530664e-1I <- {alpha = 3/2, chi = 1/23^(1/2)+1/2I, v = 1/23^(1/2)+1/2I, w = -1/2+1/2I3^(1/2)}`	Failed [294 / 300] `{Complex[0.2887554393029954, -0.22310978722682606] <- {Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.8740447527972026, 0.09051196331992012] <- {Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.23.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{iv\cos@@{\alpha}} = \frac{\EulerGamma@{\nu}}{(\tfrac{1}{2}v)^{\nu}}\*\sum_{k=0}^{\infty}(\nu+k)i^{k}\BesselJ{\nu+k}@{v}\ultrasphpoly{\nu}{k}@{\cos@@{\alpha}}}	`exp(Ivcos(alpha)) = (GAMMA(nu))/(((1)/(2)v)^(nu)) sum((nu + k)* (I)^(k)* BesselJ(nu + k, v)*GegenbauerC(k, nu, cos(alpha)), k = 0..infinity)`	`Exp[IvCos[\[Alpha]]] == Divide[Gamma[\[Nu]],(Divide[1,2]v)^\[Nu]] Sum[(\[Nu]+ k)* (I)^(k)* BesselJ[\[Nu]+ k, v]*GegenbauerC[k, \[Nu], Cos[\[Alpha]]], {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Failure	Skipped - Because timed out	Skipped - Because timed out
10.23.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\tfrac{1}{2}z)^{\nu} = \sum_{k=0}^{\infty}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\BesselJ{\nu+2k}@{z}}	`((1)/(2)z)^(nu) = sum(((nu + 2k)* GAMMA(nu + k))/(factorial(k))BesselJ(nu + 2k, z), k = 0..infinity)`	`(Divide[1,2]z)^\[Nu] == Sum[Divide[(\[Nu]+ 2k)* Gamma[\[Nu]+ k],(k)!]BesselJ[\[Nu]+ 2k, z], {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Successful	Skipped - Because timed out	Successful [Tested: 7]
10.23.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}-\frac{4}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{\BesselJ{2k}@{z}}{k}}	`BesselY(0, z) = (2)/(Pi)(ln((1)/(2)z)+ gamma)* BesselJ(0, z)-(4)/(Pi)sum((- 1)^(k)(BesselJ(2*k, z))/(k), k = 1..infinity)`	`BesselY[0, z] == Divide[2,Pi](Log[Divide[1,2]z]+ EulerGamma)* BesselJ[0, z]-Divide[4,Pi]Sum[(- 1)^(k)Divide[BesselJ[2*k, z],k], {k, 1, Infinity}, GenerateConditions->None]`	Aborted	Successful	Successful [Tested: 7]	Successful [Tested: 7]
10.23.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{n}@{z} = -\frac{n!(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}\BesselJ{k}@{z}}{k!(n-k)}+\frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\BesselJ{n}@{z}-\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{(n+2k)\BesselJ{n+2k}@{z}}{k(n+k)}}	`BesselY(n, z) = -(factorial(n)((1)/(2)z)^(- n))/(Pi)sum((((1)/(2)z)^(k)* BesselJ(k, z))/(factorial(k)(n - k)), k = 0..n - 1)+(2)/(Pi)(ln((1)/(2)z)- Psi(n + 1)) BesselJ(n, z)-(2)/(Pi)sum((- 1)^(k)((n + 2k) BesselJ(n + 2k, z))/(k(n + k)), k = 1..infinity)`	`BesselY[n, z] == -Divide[(n)!(Divide[1,2]z)^(- n),Pi]Sum[Divide[(Divide[1,2]z)^(k)* BesselJ[k, z],(k)!(n - k)], {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi](Log[Divide[1,2]z]- PolyGamma[n + 1]) BesselJ[n, z]-Divide[2,Pi]Sum[(- 1)^(k)Divide[(n + 2k) BesselJ[n + 2k, z],k(n + k)], {k, 1, Infinity}, GenerateConditions->None]`	Aborted	Failure	Manual Skip!	Failed [16 / 21] {Plus[Complex[-0.41373222494160333, 0.38808044477324316], Times[Complex[0.5513288954217921, -0.31830988618379064], DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[Times[-1, ], 1], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], []], Times[Plus[4, Times[12, ], Times[12, Power[, 2]], Times[4, Power[, 3]], Times[-4, 1], Times[-8, , 1], Times[-4, Power[, 2], 1], Times[, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-1, 1, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], [Plus[1, ]]], Times[4, Plus[1, ], Plus[-5, Times[-6, ], Times[-2, Power[, 2]], Times[3, 1], Times[2, , 1]], [Plus[2, ]]], Times[-4, Plus[1, ], Plus[2, ], Plus[-2, Times[-1, ], 1], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[1, 2], Power[Plus[-1, 1],
10.24.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(x^{2}+\nu^{2})w = 0}	`(x)^(2)* diff(w, [x$(2)])+ xdiff(w, x)+((x)^(2)+ (nu)^(2)) w = 0`	`(x)^(2)* D[w, {x, 2}]+ xD[w, x]+((x)^(2)+ \[Nu]^(2)) w == 0`	Failure	Failure	Failed [300 / 300] `300/300]: [[1.948557159+2.125000000I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 3/2}` `.2165063513+1.125000001I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 1/2}`	Failed [300 / 300] `{Complex[1.9485571585149875, 2.125] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.948557158514987, 0.12499999999999989] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.24#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJimag{\nu}@{x} = \sech@{\tfrac{1}{2}\pi\nu}\realpart@{\BesselJ{i\nu}@{x}}}	`sech((1/2)Pi(nu))Re(BesselJ(I(nu), x)) = sech((1)/(2)Pinu)Re(BesselJ(Inu, x))`	`Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]] == Sech[Divide[1,2]Pi\[Nu]]Re[BesselJ[I\[Nu], x]]`	Successful	Successful	-	Successful [Tested: 30]
10.24#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{\nu}@{x} = \sech@{\tfrac{1}{2}\pi\nu}\realpart@{\BesselY{i\nu}@{x}}}	`sech((1/2)Pi(nu))Re(BesselY(I(nu), x)) = sech((1)/(2)Pinu)Re(BesselY(Inu, x))`	`Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]] == Sech[Divide[1,2]Pi\[Nu]]Re[BesselY[I\[Nu], x]]`	Successful	Successful	-	Successful [Tested: 30]
10.24.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{1+i\nu} = \left(\frac{\pi\nu}{\sinh@{\pi\nu}}\right)^{\frac{1}{2}}e^{i\gamma_{\nu}}}	`GAMMA(1 + Inu) = ((Pinu)/(sinh(Pinu)))^((1)/(2)) exp(I*gamma[nu])`	`Gamma[1 + I\[Nu]] == (Divide[Pi\[Nu],Sinh[Pi\[Nu]]])^(Divide[1,2]) Exp[I*Subscript[\[Gamma], \[Nu]]]`	Failure	Failure	Failed [300 / 300] `300/300]: [[.131682196e-1-.6479738907I <- {gamma = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, gamma[nu] = 1/23^(1/2)+1/2I}` `.2393622021-.2867640040I <- {gamma = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, gamma[nu] = -1/2+1/2I3^(1/2)}`	Failed [300 / 300] `{Complex[0.013168219691258531, -0.6479738909120968] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.23936220222535412, -0.28676400411697583] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[γ, ν], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.24#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJimag{-\nu}@{x} = \BesselJimag{\nu}@{x}}	`sech((1/2)Pi(- nu))Re(BesselJ(I(- nu), x)) = sech((1/2)Pi(nu))Re(BesselJ(I(nu), x))`	`Sech[1/2 Pi - \[Nu]] Re[BesselJ[I - \[Nu], x]] == Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]]`	Failure	Failure	Failed [12 / 30] `12/30]: [[.1765981285-.1547836875I <- {nu = 1/23^(1/2)+1/2I, x = 3/2}` `-1.059084556+.9282601935I <- {nu = 1/23^(1/2)+1/2I, x = 1/2}`	Failed [30 / 30] `{Complex[-0.6353785354467336, 0.04153700144653363] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.2910880978413849, 0.681683596996288] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.24#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{-\nu}@{x} = \BesselYimag{\nu}@{x}}	`sech((1/2)Pi(- nu))Re(BesselY(I(- nu), x)) = sech((1/2)Pi(nu))Re(BesselY(I(nu), x))`	`Sech[1/2 Pi - \[Nu]] Re[BesselY[I - \[Nu], x]] == Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]]`	Failure	Failure	Failed [12 / 30] `12/30]: [[-.6730010946+.5898680353I <- {nu = 1/23^(1/2)+1/2I, x = 3/2}` `-.1980888923+.1736197856I <- {nu = 1/23^(1/2)+1/2I, x = 1/2}`	Failed [30 / 30] `{Complex[0.16541121369118172, 0.7534126929509344] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.3242468905843751, -0.9796849117084342] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.24.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\BesselJimag{\nu}@{x},\BesselYimag{\nu}@{x}} = 2/(\pi x)}	`(sech((1/2)Pi(nu))Re(BesselJ(I(nu), x)))diff(sech((1/2)Pi(nu))Re(BesselY(I(nu), x)), x)-diff(sech((1/2)Pi(nu))Re(BesselJ(I(nu), x)), x)(sech((1/2)Pi(nu))Re(BesselY(I(nu), x))) = 2/(Pi*x)`	`Wronskian[{Sech[1/2 Pi \[Nu]] Re[BesselJ[I \[Nu], x]], Sech[1/2 Pi \[Nu]] Re[BesselY[I \[Nu], x]]}, x] == 2/(Pi*x)`	Failure	Failure	Failed [12 / 30] `12/30]: [[-.3214564733-.7786157192I <- {nu = 1/23^(1/2)+1/2I, x = 3/2}` `-.6431025084-4.765445687I <- {nu = 1/23^(1/2)+1/2I, x = 1/2}`	Failed [30 / 30] `{Plus[-0.4244131815783876, Times[Complex[0.017184424665049866, -0.12995814793225188], Plus[Times[Complex[5.94457417937745, -0.08806734388290616], Derivative[1][Re][Complex[0.5424102683642863, 1.3820413572565333]]], Times[Complex[0.04670634387761448, 2.0064149502593187], Derivative[1][Re][Complex[1.5013396639532606, -0.5145465005058608]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[-0.4244131815783876, Times[Complex[-0.5062208144169521, 0.3689208146583662], Plus[Times[Complex[1.2690034139339206, -1.428145592425075], Derivative[1][Re][Complex[-0.5230512553281585, -0.7250724679588263]]], Times[Complex[0.9907135967899046, 0.5862869255257461], Derivative[1][Re][Complex[0.9118063408652576, -0.381897212811936]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.24.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselYimag{0}@{x} = \BesselY{0}@{x}}	`sech((1/2)Pi(0))Re(BesselY(I(0), x)) = BesselY(0, x)`	`Sech[1/2 Pi 0] Re[BesselY[I 0, x]] == BesselY[0, x]`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.25.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0}	`(z)^(2)* diff(w, [z$(2)])+ zdiff(w, z)-((z)^(2)+ (nu)^(2)) w = 0`	`(z)^(2)* D[w, {z, 2}]+ zD[w, z]-((z)^(2)+ \[Nu]^(2)) w == 0`	Failure	Failure	Failed [220 / 300] `220/300]: [[-.6467477718e-9-2.000000002I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `-.8660254040e-9-2.000000001I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/23^(1/2)-1/2I}`	Failed [264 / 300] `{Complex[0.0, -2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.0, -2.0] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}`
10.25.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}}	`BesselI(nu, z) = ((1)/(2)z)^(nu) sum((((1)/(4)(z)^(2))^(k))/(factorial(k)GAMMA(nu + k + 1)), k = 0..infinity)`	`BesselI[\[Nu], z] == (Divide[1,2]z)^\[Nu] Sum[Divide[(Divide[1,4](z)^(2))^(k),(k)!Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 70]
10.27.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-n}@{z} = \modBesselI{n}@{z}}	`BesselI(- n, z) = BesselI(n, z)`	`BesselI[- n, z] == BesselI[n, z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.27.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z}}	`BesselI(- nu, z) = BesselI(nu, z)+(2/ Pi)* sin(nuPi)BesselK(nu, z)`	`BesselI[- \[Nu], z] == BesselI[\[Nu], z]+(2/ Pi)* Sin[\[Nu]Pi]BesselK[\[Nu], z]`	Successful	Successful	-	Successful [Tested: 70]
10.27.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z}}	`BesselK(- nu, z) = BesselK(nu, z)`	`BesselK[- \[Nu], z] == BesselK[\[Nu], z]`	Successful	Successful	-	Successful [Tested: 70]
10.27.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}}}	`BesselK(nu, z) = (1)/(2)Pi(BesselI(- nu, z)- BesselI(nu, z))/(sin(nu*Pi))`	`BesselK[\[Nu], z] == Divide[1,2]PiDivide[BesselI[- \[Nu], z]- BesselI[\[Nu], z],Sin[\[Nu]*Pi]]`	Successful	Successful	-	Failed [14 / 70] `{Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}` `Indeterminate <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}`
10.27.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}}}	`BesselI(nu, z) = exp(- nuPiI/ 2)BesselJ(nu, zexp(+ Pi*I/ 2))`	`BesselI[\[Nu], z] == Exp[- \[Nu]PiI/ 2]BesselJ[\[Nu], zExp[+ Pi*I/ 2]]`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}}}	`BesselI(nu, z) = exp(+ nuPiI/ 2)BesselJ(nu, zexp(- Pi*I/ 2))`	`BesselI[\[Nu], z] == Exp[+ \[Nu]PiI/ 2]BesselJ[\[Nu], zExp[- Pi*I/ 2]]`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right)}	`BesselI(nu, z) = (1)/(2)exp(- nuPiI/ 2)(HankelH1(nu, zexp(+ PiI/ 2))+ HankelH2(nu, zexp(+ PiI/ 2)))`	`BesselI[\[Nu], z] == Divide[1,2]Exp[- \[Nu]PiI/ 2](HankelH1[\[Nu], zExp[+ PiI/ 2]]+ HankelH2[\[Nu], zExp[+ PiI/ 2]])`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right)}	`BesselI(nu, z) = (1)/(2)exp(+ nuPiI/ 2)(HankelH1(nu, zexp(- PiI/ 2))+ HankelH2(nu, zexp(- PiI/ 2)))`	`BesselI[\[Nu], z] == Divide[1,2]Exp[+ \[Nu]PiI/ 2](HankelH1[\[Nu], zExp[- PiI/ 2]]+ HankelH2[\[Nu], zExp[- PiI/ 2]])`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}}	`PiIBesselJ(nu, z) = exp(- nuPiI/ 2)BesselK(nu, zexp(- PiI/ 2))- exp(nuPiI/ 2)BesselK(nu, zexp(PiI/ 2))`	`PiIBesselJ[\[Nu], z] == Exp[- \[Nu]PiI/ 2]BesselK[\[Nu], zExp[- PiI/ 2]]- Exp[\[Nu]PiI/ 2]BesselK[\[Nu], zExp[PiI/ 2]]`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}}	`- PiBesselY(nu, z) = exp(- nuPiI/ 2)BesselK(nu, zexp(- PiI/ 2))+ exp(nuPiI/ 2)BesselK(nu, zexp(Pi*I/ 2))`	`- PiBesselY[\[Nu], z] == Exp[- \[Nu]PiI/ 2]BesselK[\[Nu], zExp[- PiI/ 2]]+ Exp[\[Nu]PiI/ 2]BesselK[\[Nu], zExp[Pi*I/ 2]]`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}}	`BesselY(nu, z) = exp(+(nu + 1)* PiI/ 2)BesselI(nu, zexp(- PiI/ 2))-(2/ Pi)* exp(- nuPiI/ 2)BesselK(nu, zexp(- Pi*I/ 2))`	`BesselY[\[Nu], z] == Exp[+(\[Nu]+ 1)* PiI/ 2]BesselI[\[Nu], zExp[- PiI/ 2]]-(2/ Pi)* Exp[- \[Nu]PiI/ 2]BesselK[\[Nu], zExp[- Pi*I/ 2]]`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.27.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}}}	`BesselY(nu, z) = exp(-(nu + 1)* PiI/ 2)BesselI(nu, zexp(+ PiI/ 2))-(2/ Pi)* exp(+ nuPiI/ 2)BesselK(nu, zexp(+ Pi*I/ 2))`	`BesselY[\[Nu], z] == Exp[-(\[Nu]+ 1)* PiI/ 2]BesselI[\[Nu], zExp[+ PiI/ 2]]-(2/ Pi)* Exp[+ \[Nu]PiI/ 2]BesselK[\[Nu], zExp[+ Pi*I/ 2]]`	Failure	Failure	Successful [Tested: 50]	Successful [Tested: 50]
10.28.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselI{\nu}@{z},\modBesselI{-\nu}@{z}} = \modBesselI{\nu}@{z}\modBesselI{-\nu-1}@{z}-\modBesselI{\nu+1}@{z}\modBesselI{-\nu}@{z}}	`(BesselI(nu, z))diff(BesselI(- nu, z), z)-diff(BesselI(nu, z), z)(BesselI(- nu, z)) = BesselI(nu, z)BesselI(- nu - 1, z)- BesselI(nu + 1, z)BesselI(- nu, z)`	`Wronskian[{BesselI[\[Nu], z], BesselI[- \[Nu], z]}, z] == BesselI[\[Nu], z]BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]BesselI[- \[Nu], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.28.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselI{-\nu-1}@{z}-\modBesselI{\nu+1}@{z}\modBesselI{-\nu}@{z} = -2\sin@{\nu\pi}/(\pi z)}	`BesselI(nu, z)BesselI(- nu - 1, z)- BesselI(nu + 1, z)BesselI(- nu, z) = - 2sin(nuPi)/(Pi*z)`	`BesselI[\[Nu], z]BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]BesselI[- \[Nu], z] == - 2Sin[\[Nu]Pi]/(Pi*z)`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.28.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselK{\nu}@{z},\modBesselI{\nu}@{z}} = \modBesselI{\nu}@{z}\modBesselK{\nu+1}@{z}+\modBesselI{\nu+1}@{z}\modBesselK{\nu}@{z}}	`(BesselK(nu, z))diff(BesselI(nu, z), z)-diff(BesselK(nu, z), z)(BesselI(nu, z)) = BesselI(nu, z)BesselK(nu + 1, z)+ BesselI(nu + 1, z)BesselK(nu, z)`	`Wronskian[{BesselK[\[Nu], z], BesselI[\[Nu], z]}, z] == BesselI[\[Nu], z]BesselK[\[Nu]+ 1, z]+ BesselI[\[Nu]+ 1, z]BesselK[\[Nu], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 70]
10.28.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselK{\nu+1}@{z}+\modBesselI{\nu+1}@{z}\modBesselK{\nu}@{z} = 1/z}	`BesselI(nu, z)BesselK(nu + 1, z)+ BesselI(nu + 1, z)BesselK(nu, z) = 1/ z`	`BesselI[\[Nu], z]BesselK[\[Nu]+ 1, z]+ BesselI[\[Nu]+ 1, z]BesselK[\[Nu], z] == 1/ z`	Failure	Successful	Successful [Tested: 70]	Successful [Tested: 70]
10.29#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}'@{z} = \modBesselI{1}@{z}}	`diff( BesselI(0, z), z$(1) ) = BesselI(1, z)`	`D[BesselI[0, z], {z, 1}] == BesselI[1, z]`	Successful	Successful	-	Successful [Tested: 7]
10.29#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}'@{z} = -\modBesselK{1}@{z}}	`diff( BesselK(0, z), z$(1) ) = - BesselK(1, z)`	`D[BesselK[0, z], {z, 1}] == - BesselK[1, z]`	Successful	Successful	-	Successful [Tested: 7]
10.31.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}(-\tfrac{1}{4}z^{2})^{k}+(-1)^{n+1}\ln@{\tfrac{1}{2}z}\modBesselI{n}@{z}+(-1)^{n}\tfrac{1}{2}(\tfrac{1}{2}z)^{n}\sum_{k=0}^{\infty}\left(\digamma@{k+1}+\digamma@{n+k+1}\right)\frac{(\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}}	`BesselK(n, z) = (1)/(2)((1)/(2)z)^(- n)* sum((factorial(n - k - 1))/(factorial(k))(-(1)/(4)(z)^(2))^(k), k = 0..n - 1)+(- 1)^(n + 1)* ln((1)/(2)z)BesselI(n, z)+(- 1)^(n)(1)/(2)((1)/(2)z)^(n) sum((Psi(k + 1)+ Psi(n + k + 1))(((1)/(4)(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity)`	`BesselK[n, z] == Divide[1,2](Divide[1,2]z)^(- n)* Sum[Divide[(n - k - 1)!,(k)!](-Divide[1,4](z)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n + 1)* Log[Divide[1,2]z]BesselI[n, z]+(- 1)^(n)Divide[1,2](Divide[1,2]z)^(n) Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])Divide[(Divide[1,4](z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Aborted	Skipped - Because timed out	Failed [6 / 21] {Plus[0.6666666666666666, Times[-0.6666666666666666, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Power[1.5, 2]], [Plus[2, ]]], Times[-1, Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[-4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[-1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[-32, 3], Power[1.5, -6], Plus[3, Times[Rational[-1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]} `Plus[0.38888888888888906, Times[0.5, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Power[1.5, 2]], [Plus[2, ]]], Times[-1, Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equ`
10.31.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\modBesselI{0}@{z}+\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}+(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}+\dotsi}	`BesselK(0, z) = -(ln((1)/(2)z)+ gamma) BesselI(0, z)+((1)/(4)(z)^(2))/((factorial(1))^(2))+(1 +(1)/(2))(((1)/(4)(z)^(2))^(2))/((factorial(2))^(2))+(1 +(1)/(2)+(1)/(3))(((1)/(4)*(z)^(2))^(3))/((factorial(3))^(2))+ ..`	`BesselK[0, z] == -(Log[Divide[1,2]z]+ EulerGamma) BesselI[0, z]+Divide[Divide[1,4](z)^(2),((1)!)^(2)]+(1 +Divide[1,2])Divide[(Divide[1,4](z)^(2))^(2),((2)!)^(2)]+(1 +Divide[1,2]+Divide[1,3])Divide[(Divide[1,4]*(z)^(2))^(3),((3)!)^(2)]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-6.985673039111573^-6, -1.2369744460005716^-5], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-7.140527721077872^-6, -1.2101549865001227^-5], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.31.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z}\modBesselI{\mu}@{z} = (\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}\EulerGamma@{\mu+k+1}}}	`BesselI(nu, z)BesselI(mu, z) = ((1)/(2)z)^(nu + mu)* sum((nu + mu + k + 1[k]((1)/(4)(z)^(2))^(k))/(factorial(k)GAMMA(nu + k + 1)GAMMA(mu + k + 1)), k = 0..infinity)`	`BesselI[\[Nu], z]BesselI[\[Mu], z] == (Divide[1,2]z)^(\[Nu]+ \[Mu])* Sum[Divide[Subscript[\[Nu]+ \[Mu]+ k + 1, k](Divide[1,4](z)^(2))^(k),(k)!Gamma[\[Nu]+ k + 1]Gamma[\[Mu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
10.32.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta}}	`BesselI(0, z) = (1)/(Pi)int(exp(+ zcos(theta)), theta = 0..Pi)`	`BesselI[0, z] == Divide[1,Pi]Integrate[Exp[+ zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.32.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta}}	`BesselI(0, z) = (1)/(Pi)int(exp(- zcos(theta)), theta = 0..Pi)`	`BesselI[0, z] == Divide[1,Pi]Integrate[Exp[- zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.32.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}}	`(1)/(Pi)int(exp(+ zcos(theta)), theta = 0..Pi) = (1)/(Pi)int(cosh(zcos(theta)), theta = 0..Pi)`	`Divide[1,Pi]Integrate[Exp[+ zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]Integrate[Cosh[zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Successful [Tested: 7]
10.32.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}}	`(1)/(Pi)int(exp(- zcos(theta)), theta = 0..Pi) = (1)/(Pi)int(cosh(zcos(theta)), theta = 0..Pi)`	`Divide[1,Pi]Integrate[Exp[- zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]Integrate[Cosh[zCos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Successful [Tested: 7]
10.32.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}}	`BesselI(nu, z) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(+ zcos(theta))(sin(theta))^(2nu), theta = 0..Pi)`	`BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[+ zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 35]
10.32.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}}	`BesselI(nu, z) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(- zcos(theta))(sin(theta))^(2nu), theta = 0..Pi)`	`BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 35]
10.32.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}}	`(((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(+ zcos(theta))(sin(theta))^(2nu), theta = 0..Pi) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int((1 - (t)^(2))^(nu -(1)/(2)) exp(+ z*t), t = - 1..1)`	`Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[+ zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2]) Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 35]
10.32.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}}	`(((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int(exp(- zcos(theta))(sin(theta))^(2nu), theta = 0..Pi) = (((1)/(2)z)^(nu))/((Pi)^((1)/(2)) GAMMA(nu +(1)/(2)))int((1 - (t)^(2))^(nu -(1)/(2)) exp(- z*t), t = - 1..1)`	`Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCos[\[Theta]]](Sin[\[Theta]])^(2\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]z)^\[Nu],(Pi)^(Divide[1,2]) Gamma[\[Nu]+Divide[1,2]]]Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2]) Exp[- z*t], {t, - 1, 1}, GenerateConditions->None]`	Error	Aborted	Skip - symbolical successful subtest	Successful [Tested: 35]
10.32.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}}	`BesselI(n, z) = (1)/(Pi)int(exp(zcos(theta))cos(ntheta), theta = 0..Pi)`	`BesselI[n, z] == Divide[1,Pi]Integrate[Exp[zCos[\[Theta]]]Cos[n\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 21]	Skipped - Because timed out
10.32.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}}	`BesselI(nu, z) = (1)/(Pi)int(exp(zcos(theta))cos(nutheta), theta = 0..Pi)-(sin(nuPi))/(Pi)int(exp(- zcosh(t)- nut), t = 0..infinity)`	`BesselI[\[Nu], z] == Divide[1,Pi]Integrate[Exp[zCos[\[Theta]]]Cos[\[Nu]\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]Pi],Pi]Integrate[Exp[- zCosh[t]- \[Nu]t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}}	`BesselK(0, z) = -(1)/(Pi)int(exp(+ zcos(theta))(gamma + ln(2z*(sin(theta))^(2))), theta = 0..Pi)`	`BesselK[0, z] == -Divide[1,Pi]Integrate[Exp[+ zCos[\[Theta]]](EulerGamma + Log[2z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]`	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}}	`BesselK(0, z) = -(1)/(Pi)int(exp(- zcos(theta))(gamma + ln(2z*(sin(theta))^(2))), theta = 0..Pi)`	`BesselK[0, z] == -Divide[1,Pi]Integrate[Exp[- zCos[\[Theta]]](EulerGamma + Log[2z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]`	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}}	`BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity)`	`BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]`	Successful	Aborted	-	Skipped - Because timed out
10.32.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}}	`int(cos(xsinh(t)), t = 0..infinity) = int((cos(xt))/(sqrt((t)^(2)+ 1)), t = 0..infinity)`	`Integrate[Cos[xSinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[xt],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None]`	Successful	Aborted	-	Skipped - Because timed out
10.32.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}}	`BesselK(nu, x) = sec((1)/(2)nuPi)int(cos(xsinh(t))cosh(nut), t = 0..infinity)`	`BesselK[\[Nu], x] == Sec[Divide[1,2]\[Nu]Pi]Integrate[Cos[xSinh[t]]Cosh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None]`	Successful	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}}	`sec((1)/(2)nuPi)int(cos(xsinh(t))cosh(nut), t = 0..infinity) = csc((1)/(2)nuPi)int(sin(xsinh(t))sinh(nut), t = 0..infinity)`	`Sec[Divide[1,2]\[Nu]Pi]Integrate[Cos[xSinh[t]]Cosh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]\[Nu]Pi]Integrate[Sin[xSinh[t]]Sinh[\[Nu]t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}}	`BesselK(nu, z) = ((Pi)^((1)/(2))((1)/(2)z)^(nu))/(GAMMA(nu +(1)/(2)))int(exp(- zcosh(t))(sinh(t))^(2nu), t = 0..infinity)`	`BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCosh[t]](Sinh[t])^(2\[Nu]), {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}}	`((Pi)^((1)/(2))((1)/(2)z)^(nu))/(GAMMA(nu +(1)/(2)))int(exp(- zcosh(t))(sinh(t))^(2nu), t = 0..infinity) = ((Pi)^((1)/(2))((1)/(2)z)^(nu))/(GAMMA(nu +(1)/(2)))int(exp(- zt)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1..infinity)`	`Divide[(Pi)^(Divide[1,2])(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zCosh[t]](Sinh[t])^(2\[Nu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Pi)^(Divide[1,2])(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]Integrate[Exp[- zt]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1, Infinity}, GenerateConditions->None]`	Error	Aborted	Skip - symbolical successful subtest	Skipped - Because timed out
10.32.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}}	`BesselK(nu, z) = int(exp(- zcosh(t))cosh(nu*t), t = 0..infinity)`	`BesselK[\[Nu], z] == Integrate[Exp[- zCosh[t]]Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}}	`BesselK(nu, z) = (1)/(2)((1)/(2)z)^(nu)* int(exp(- t -((z)^(2))/(4t))(1)/((t)^(nu + 1)), t = 0..infinity)`	`BesselK[\[Nu], z] == Divide[1,2](Divide[1,2]z)^\[Nu]* Integrate[Exp[- t -Divide[(z)^(2),4t]]Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 40]
10.32.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}}	`BesselK(nu, x(x + yI)) = (GAMMA(nu +(1)/(2))(2(x + yI))^(nu))/((Pi)^((1)/(2)) (x)^(nu))int((cos(xt))/(((t)^(2)+(x + y*I)^(2))^(nu +(1)/(2))), t = 0..infinity)`	`BesselK[\[Nu], x(x + yI)] == Divide[Gamma[\[Nu]+Divide[1,2]](2(x + yI))^\[Nu],(Pi)^(Divide[1,2]) (x)^\[Nu]]Integrate[Divide[Cos[xt],((t)^(2)+(x + y*I)^(2))^(\[Nu]+Divide[1,2])], {t, 0, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.32.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}}	`BesselI(nu, z) = (1)/(2PiI)int(exp(zcosh(t)- nut), t = infinity - IPi..infinity + I*Pi)`	`BesselI[\[Nu], z] == Divide[1,2PiI]Integrate[Exp[zCosh[t]- \[Nu]t], {t, Infinity - IPi, Infinity + I*Pi}, GenerateConditions->None]`	Error	Failure	-	Failed [50 / 50] `{Complex[0.5303418993681409, 0.010453999760907294] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.7664848208906112, 0.1468422559210476] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.32.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}}	`BesselK(nu, z) = (((1)/(2)z)^(nu))/(4PiI)int(GAMMA(t)GAMMA(t - nu)((1)/(2)z)^(- 2t), t = c - Iinfinity..c + Iinfinity)`	`BesselK[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],4PiI]Integrate[Gamma[t]Gamma[t - \[Nu]](Divide[1,2]z)^(- 2t), {t, c - IInfinity, c + IInfinity}, GenerateConditions->None]`	Failure	Aborted	Failed [300 / 300] `300/300]: [[.5663982443-.3181066824I <- {c = -3/2, nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `-1.434992817-2.759712160I <- {c = -3/2, nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}`	Skipped - Because timed out
10.32.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}}	`BesselK(nu, z) = (1)/(2(Pi)^(2) I)((Pi)/(2z))^((1)/(2))* exp(- z)cos(nuPi)* int(GAMMA(t)GAMMA((1)/(2)- t - nu)GAMMA((1)/(2)- t + nu)(2z)^(t), t = - Iinfinity..Iinfinity)`	`BesselK[\[Nu], z] == Divide[1,2(Pi)^(2) I](Divide[Pi,2z])^(Divide[1,2])* Exp[- z]Cos[\[Nu]Pi]* Integrate[Gamma[t]Gamma[Divide[1,2]- t - \[Nu]]Gamma[Divide[1,2]- t + \[Nu]](2z)^(t), {t, - IInfinity, IInfinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}}	`BesselI(mu, z)BesselI(nu, z) = (2)/(Pi)int(BesselI(mu + nu, 2zcos(theta))cos((mu - nu) theta), theta = 0..(1)/(2)*Pi)`	`BesselI[\[Mu], z]BesselI[\[Nu], z] == Divide[2,Pi]Integrate[BesselI[\[Mu]+ \[Nu], 2zCos[\[Theta]]]Cos[(\[Mu]- \[Nu]) \[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.32.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}}	`BesselI(mu, x)BesselK(nu, x) = int(BesselJ(mu + nu, 2xsinh(t))exp((- mu + nu)* t), t = 0..infinity)`	`BesselI[\[Mu], x]BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]+ \[Nu], 2xSinh[t]]Exp[(- \[Mu]+ \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.32.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}}	`BesselI(mu, x)BesselK(nu, x) = int(BesselJ(mu - nu, 2xsinh(t))exp((- mu - nu)* t), t = 0..infinity)`	`BesselI[\[Mu], x]BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]- \[Nu], 2xSinh[t]]Exp[(- \[Mu]- \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.32.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}}	`BesselK(mu, z)BesselK(nu, z) = 2int(BesselK(mu + nu, 2zcosh(t))cosh((mu - nu) t), t = 0..infinity)`	`BesselK[\[Mu], z]BesselK[\[Nu], z] == 2Integrate[BesselK[\[Mu]+ \[Nu], 2zCosh[t]]Cosh[(\[Mu]- \[Nu]) t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}}	`BesselK(mu, z)BesselK(nu, z) = 2int(BesselK(mu - nu, 2zcosh(t))cosh((mu + nu) t), t = 0..infinity)`	`BesselK[\[Mu], z]BesselK[\[Nu], z] == 2Integrate[BesselK[\[Mu]- \[Nu], 2zCosh[t]]Cosh[(\[Mu]+ \[Nu]) t], {t, 0, Infinity}, GenerateConditions->None]`	Failure	Aborted	Manual Skip!	Skipped - Because timed out
10.32.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}}	`BesselK(nu, z)BesselK(nu, zeta) = (1)/(2)int(exp(-(t)/(2)-((z)^(2)+ (zeta)^(2))/(2t))BesselK(nu, ((zzeta)/(t)))*(1)/(t), t = 0..infinity)`	`BesselK[\[Nu], z]BesselK[\[Nu], \[Zeta]] == Divide[1,2]Integrate[Exp[-Divide[t,2]-Divide[(z)^(2)+ \[Zeta]^(2),2t]]BesselK[\[Nu], (Divide[z\[Zeta],t])]*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]`	Translation Error	Translation Error	-	-
10.32.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}}	`BesselK(mu, z)BesselK(nu, z) = (1)/(8PiI)int((GAMMA(t +(1)/(2)mu +(1)/(2)nu)GAMMA(t +(1)/(2)mu -(1)/(2)nu)GAMMA(t -(1)/(2)mu +(1)/(2)nu)GAMMA(t -(1)/(2)mu -(1)/(2)nu))/(GAMMA(2t))((1)/(2)z)^(- 2t), t = c - Iinfinity..c + I*infinity)`	`BesselK[\[Mu], z]BesselK[\[Nu], z] == Divide[1,8PiI]Integrate[Divide[Gamma[t +Divide[1,2]\[Mu]+Divide[1,2]\[Nu]]Gamma[t +Divide[1,2]\[Mu]-Divide[1,2]\[Nu]]Gamma[t -Divide[1,2]\[Mu]+Divide[1,2]\[Nu]]Gamma[t -Divide[1,2]\[Mu]-Divide[1,2]\[Nu]],Gamma[2t]](Divide[1,2]z)^(- 2t), {t, c - IInfinity, c + I*Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skip - No test values generated

@@ Line 81: / Line 81: @@
 | [https://dlmf.nist.gov/10.6.E10 10.6.E10] || [[Item:Q3052|<math>p_{\nu}s_{\nu}-q_{\nu}r_{\nu} = 4/(\pi^{2}ab)</math>]] || <code>p[nu]*s[nu]- q[nu]*r[nu] = 4/((Pi)^(2)* a*b)</code> || <code>Subscript[p, \[Nu]]*Subscript[s, \[Nu]]- Subscript[q, \[Nu]]*Subscript[r, \[Nu]] == 4/((Pi)^(2)* a*b)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/10.8.E1 10.8.E1] || [[Item:Q3063|<math>\BesselY{n}@{z} = -\frac{(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+\frac{2}{\pi}\ln@{\tfrac{1}{2}z}\BesselJ{n}@{z}-\frac{(\tfrac{1}{2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(\digamma@{k+1}+\digamma@{n+k+1})\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}</math>]] || <code>BesselY(n, z) = -(((1)/(2)*z)^(- n))/(Pi)*sum((factorial(n - k - 1))/(factorial(k))*((1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(2)/(Pi)*ln((1)/(2)*z)*BesselJ(n, z)-(((1)/(2)*z)^(n))/(Pi)*sum((Psi(k + 1)+ Psi(n + k + 1))*((-(1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity)</code> || <code>BesselY[n, z] == -Divide[(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(n - k - 1)!,(k)!]*(Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]*Log[Divide[1,2]*z]*BesselJ[n, z]-Divide[(Divide[1,2]*z)^(n),Pi]*Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(-Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><code>{Plus[-0.4244131815783875, Times[0.4244131815783876, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[32, 3], Power[1.5, -6], Plus[3, Times[Rational[1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]}</code><br><code>Plus[-0.8841941282883073, Times[0.3183098861837907, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[32, 3], Power[1.5, -6], Plus[3, Times[Rational[1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][2.0]]], {Rule[n, 2], Rule[z, 1.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.8.E1 10.8.E1] || [[Item:Q3063|<math>\BesselY{n}@{z} = -\frac{(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+\frac{2}{\pi}\ln@{\tfrac{1}{2}z}\BesselJ{n}@{z}-\frac{(\tfrac{1}{2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(\digamma@{k+1}+\digamma@{n+k+1})\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}</math>]] || <code>BesselY(n, z) = -(((1)/(2)*z)^(- n))/(Pi)*sum((factorial(n - k - 1))/(factorial(k))*((1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(2)/(Pi)*ln((1)/(2)*z)*BesselJ(n, z)-(((1)/(2)*z)^(n))/(Pi)*sum((Psi(k + 1)+ Psi(n + k + 1))*((-(1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity)</code> || <code>BesselY[n, z] == -Divide[(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(n - k - 1)!,(k)!]*(Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]*Log[Divide[1,2]*z]*BesselJ[n, z]-Divide[(Divide[1,2]*z)^(n),Pi]*Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(-Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><code>{Plus[-0.4244131815783875, Times[0.4244131815783876, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[32, 3], Power[1.5, -6], Plus[3, Times[Rational[1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]}</code><br><code>Plus[-0.8841941282883073, Times[0.3183098861837907, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[2, ], Power[1.5, 2], [Plus[3, ]]]]</div></div>
 |-
 | [https://dlmf.nist.gov/10.8.E2 10.8.E2] || [[Item:Q3064|<math>\BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\dotsi\right)</math>]] || <code>BesselY(0, z) = (2)/(Pi)*(ln((1)/(2)*z)+ gamma)* BesselJ(0, z)+(2)/(Pi)*(((1)/(4)*(z)^(2))/((factorial(1))^(2))-(1 +(1)/(2))*(((1)/(4)*(z)^(2))^(2))/((factorial(2))^(2))+(1 +(1)/(2)+(1)/(3))*(((1)/(4)*(z)^(2))^(3))/((factorial(3))^(2))- .. )</code> || <code>BesselY[0, z] == Divide[2,Pi]*(Log[Divide[1,2]*z]+ EulerGamma)* BesselJ[0, z]+Divide[2,Pi]*(Divide[Divide[1,4]*(z)^(2),((1)!)^(2)]-(1 +Divide[1,2])*Divide[(Divide[1,4]*(z)^(2))^(2),((2)!)^(2)]+(1 +Divide[1,2]+Divide[1,3])*Divide[(Divide[1,4]*(z)^(2))^(3),((3)!)^(2)]- \[Ellipsis])</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.08653583575184755, 0.12491815695491987], Times[-0.6366197723675814, Plus[Complex[0.13592303240740744, 0.19620888054491187], Times[-1.0, …]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.07160606681826986, -0.15074612001799426], Times[-0.6366197723675814, Plus[Complex[-0.11248553240740736, -0.23680382134730746], Times[-1.0, …]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.8.E3 10.8.E3] || [[Item:Q3065|<math>\BesselJ{\nu}@{z}\BesselJ{\mu}@{z} = (\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}\EulerGamma@{\mu+k+1}}</math>]] || <code>BesselJ(nu, z)*BesselJ(mu, z) = ((1)/(2)*z)^(nu + mu)* sum((nu + mu + k + 1[k]*(-(1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)*GAMMA(mu + k + 1)), k = 0..infinity)</code> || <code>BesselJ[\[Nu], z]*BesselJ[\[Mu], z] == (Divide[1,2]*z)^(\[Nu]+ \[Mu])* Sum[Divide[Subscript[\[Nu]+ \[Mu]+ k + 1, k]*(-Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]*Gamma[\[Mu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.18482793500467376, -0.06270111308873656], Times[Complex[-0.17426361621858172, -0.037827155645948574], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -2], Subscript[Plus[1, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], k]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.47215054540190965, -0.036453907426047115], Times[Complex[-0.27630938504679325, 0.26010894184513544], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k]], -1], Subscript[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], k]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.8.E3 10.8.E3] || [[Item:Q3065|<math>\BesselJ{\nu}@{z}\BesselJ{\mu}@{z} = (\tfrac{1}{2}z)^{\nu+\mu}\sum_{k=0}^{\infty}\frac{(\nu+\mu+k+1)_{k}(-\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}\EulerGamma@{\mu+k+1}}</math>]] || <code>BesselJ(nu, z)*BesselJ(mu, z) = ((1)/(2)*z)^(nu + mu)* sum((nu + mu + k + 1[k]*(-(1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)*GAMMA(mu + k + 1)), k = 0..infinity)</code> || <code>BesselJ[\[Nu], z]*BesselJ[\[Mu], z] == (Divide[1,2]*z)^(\[Nu]+ \[Mu])* Sum[Divide[Subscript[\[Nu]+ \[Mu]+ k + 1, k]*(-Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]*Gamma[\[Mu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.18482793500467376, -0.06270111308873656], Times[Complex[-0.17426361621858172, -0.037827155645948574], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -2], Subscript[Plus[1, Times[2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], k]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.47215054540190965, -0.036453907426047115], Times[Complex[-0.27630938504679325, 0.26010894184513544], NSum[Times[Power[Times[Rational[-1, 4], Power[E, Times[Complex[0, Rational[1, 3]], Pi]]], k], Power[Factorial[k], -1], Power[Gamma[Plus[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k]], -1], Power[Gamma[Plus[1, P</div></div>
 |-
 | [https://dlmf.nist.gov/10.9.E1 10.9.E1] || [[Item:Q3066|<math>\BesselJ{0}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta}</math>]] || <code>BesselJ(0, z) = (1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi)</code> || <code>BesselJ[0, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 7]<div class="mw-collapsible-content"><code>{Complex[0.1024204169391214, -0.20298051839359257] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.35155242920280916, 0.2300320660405755] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 91: / Line 91: @@
 | [https://dlmf.nist.gov/10.9.E1 10.9.E1] || [[Item:Q3066|<math>\frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}\diff{\theta}</math>]] || <code>(1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi) = (1)/(Pi)*int(cos(z*cos(theta)), theta = 0..Pi)</code> || <code>Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cos[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.9.E2 10.9.E2] || [[Item:Q3067|<math>\BesselJ{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta}</math>]] || <code>BesselJ(n, z) = (1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi)</code> || <code>BesselJ[n, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.9.E2 10.9.E2] || [[Item:Q3067|<math>\BesselJ{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta}</math>]] || <code>BesselJ(n, z) = (1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi)</code> || <code>BesselJ[n, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.9.E2 10.9.E2] || [[Item:Q3067|<math>\frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta} = \frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</math>]] || <code>(1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi) = ((I)^(- n))/(Pi)*int(exp(I*z*cos(theta))*cos(n*theta), theta = 0..Pi)</code> || <code>Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(I)^(- n),Pi]*Integrate[Exp[I*z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 7] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E2 10.9.E2] || [[Item:Q3067|<math>\frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-n\theta}\diff{\theta} = \frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</math>]] || <code>(1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi) = ((I)^(- n))/(Pi)*int(exp(I*z*cos(theta))*cos(n*theta), theta = 0..Pi)</code> || <code>Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(I)^(- n),Pi]*Integrate[Exp[I*z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 7] || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9.E3 10.9.E3] || [[Item:Q3068|<math>\BesselY{0}@{z} = \frac{4}{\pi^{2}}\int_{0}^{\frac{1}{2}\pi}\cos@{z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z\sin^{2}@@{\theta}}\right)\diff{\theta}</math>]] || <code>BesselY(0, z) = (4)/((Pi)^(2))*int(cos(z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..(1)/(2)*Pi)</code> || <code>BesselY[0, z] == Divide[4,(Pi)^(2)]*Integrate[Cos[z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]</code> || Aborted || Aborted || Successful [Tested: 7] || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.9.E4 10.9.E4] || [[Item:Q3069|<math>\BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]] || <code>BesselJ(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</code> || <code>BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Error || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 35]<div class="mw-collapsible-content"><code>{Complex[0.009683985979314524, -0.05759180507972181] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.21993206762171735, 0.08917811286212163] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</code><br></div></div>
@@ Line 101: / Line 103: @@
 | [https://dlmf.nist.gov/10.9.E5 10.9.E5] || [[Item:Q3070|<math>\BesselY{\nu}@{z} = \frac{2(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}}\left(\int_{0}^{1}(1-t^{2})^{\nu-\frac{1}{2}}\sin@{zt}\diff{t}-\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{2}}\diff{t}\right)</math>]] || <code>BesselY(nu, z) = (2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*(int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1)- int(exp(- z*t)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity))</code> || <code>BesselY[\[Nu], z] == Divide[2*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*(Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}, GenerateConditions->None]- Integrate[Exp[- z*t]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}, GenerateConditions->None])</code> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 25]<div class="mw-collapsible-content"><code>{Complex[-0.9495382353861556, 0.46093572348323536] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1.5]}</code><br><code>Complex[-0.7706973036767981, 0.20650772012904162] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.9.E6 10.9.E6] || [[Item:Q3071|<math>\BesselJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>BesselJ(nu, z) = (1)/(Pi)*int(cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*sinh(t)- nu*t), t = 0..infinity)</code> || <code>BesselJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 50]<div class="mw-collapsible-content"><code>1/50]: [[-.1812319652 <- {nu = -1/2, z = 3/2}</code><br></div></div> || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E6 10.9.E6] || [[Item:Q3071|<math>\BesselJ{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>BesselJ(nu, z) = (1)/(Pi)*int(cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*sinh(t)- nu*t), t = 0..infinity)</code> || <code>BesselJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 50]<div class="mw-collapsible-content"><code>1/50]: [[-.1812319652 <- {nu = -1/2, z = 3/2}</code><br></div></div> || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9.E7 10.9.E7] || [[Item:Q3072|<math>\BesselY{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t}+e^{-\nu t}\cos@{\nu\pi}\right)e^{-z\sinh@@{t}}\diff{t}</math>]] || <code>BesselY(nu, z) = (1)/(Pi)*int(sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t)+ exp(- nu*t)*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity)</code> || <code>BesselY[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t]+ Exp[- \[Nu]*t]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9#Ex1 10.9#Ex1] || [[Item:Q3073|<math>\BesselJ{\nu}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselJ(nu, x) = (2)/(Pi)*int(sin(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity)</code> || <code>BesselJ[\[Nu], x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9.E7 10.9.E7] || [[Item:Q3072|<math>\BesselY{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t}+e^{-\nu t}\cos@{\nu\pi}\right)e^{-z\sinh@@{t}}\diff{t}</math>]] || <code>BesselY(nu, z) = (1)/(Pi)*int(sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t)+ exp(- nu*t)*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity)</code> || <code>BesselY[\[Nu], z] == Divide[1,Pi]*Integrate[Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t]+ Exp[- \[Nu]*t]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9#Ex2 10.9#Ex2] || [[Item:Q3074|<math>\BesselY{\nu}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselY(nu, x) = -(2)/(Pi)*int(cos(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity)</code> || <code>BesselY[\[Nu], x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9#Ex1 10.9#Ex1] || [[Item:Q3073|<math>\BesselJ{\nu}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselJ(nu, x) = (2)/(Pi)*int(sin(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity)</code> || <code>BesselJ[\[Nu], x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9#Ex3 10.9#Ex3] || [[Item:Q3075|<math>\BesselJ{0}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}}\diff{t}</math>]] || <code>BesselJ(0, x) = (2)/(Pi)*int(sin(x*cosh(t)), t = 0..infinity)</code> || <code>BesselJ[0, x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9#Ex2 10.9#Ex2] || [[Item:Q3074|<math>\BesselY{\nu}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}-\tfrac{1}{2}\nu\pi}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselY(nu, x) = -(2)/(Pi)*int(cos(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity)</code> || <code>BesselY[\[Nu], x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9#Ex4 10.9#Ex4] || [[Item:Q3076|<math>\BesselY{0}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}}\diff{t}</math>]] || <code>BesselY(0, x) = -(2)/(Pi)*int(cos(x*cosh(t)), t = 0..infinity)</code> || <code>BesselY[0, x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9#Ex3 10.9#Ex3] || [[Item:Q3075|<math>\BesselJ{0}@{x} = \frac{2}{\pi}\int_{0}^{\infty}\sin@{x\cosh@@{t}}\diff{t}</math>]] || <code>BesselJ(0, x) = (2)/(Pi)*int(sin(x*cosh(t)), t = 0..infinity)</code> || <code>BesselJ[0, x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E10 10.9.E10] || [[Item:Q3077|<math>\HankelH{1}{\nu}@{z} = \frac{e^{-\frac{1}{2}\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{iz\cosh@@{t}-\nu t}\diff{t}</math>]] || <code>HankelH1(nu, z) = (exp(-(1)/(2)*nu*Pi*I))/(Pi*I)*int(exp(I*z*cosh(t)- nu*t), t = - infinity..infinity)</code> || <code>HankelH1[\[Nu], z] == Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],Pi*I]*Integrate[Exp[I*z*Cosh[t]- \[Nu]*t], {t, - Infinity, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9#Ex4 10.9#Ex4] || [[Item:Q3076|<math>\BesselY{0}@{x} = -\frac{2}{\pi}\int_{0}^{\infty}\cos@{x\cosh@@{t}}\diff{t}</math>]] || <code>BesselY(0, x) = -(2)/(Pi)*int(cos(x*cosh(t)), t = 0..infinity)</code> || <code>BesselY[0, x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E11 10.9.E11] || [[Item:Q3078|<math>\HankelH{2}{\nu}@{z} = -\frac{e^{\frac{1}{2}\nu\pi i}}{\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh@@{t}-\nu t}\diff{t}</math>]] || <code>HankelH2(nu, z) = -(exp((1)/(2)*nu*Pi*I))/(Pi*I)*int(exp(- I*z*cosh(t)- nu*t), t = - infinity..infinity)</code> || <code>HankelH2[\[Nu], z] == -Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],Pi*I]*Integrate[Exp[- I*z*Cosh[t]- \[Nu]*t], {t, - Infinity, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9#Ex5 10.9#Ex5] || [[Item:Q3079|<math>\BesselJ{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\sin@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}</math>]] || <code>BesselJ(nu, x) = (2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((sin(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity)</code> || <code>BesselJ[\[Nu], x] == Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Sin[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None]</code> || Successful || Error || - || Successful [Tested: 15]
+| [https://dlmf.nist.gov/10.9#Ex5 10.9#Ex5] || [[Item:Q3079|<math>\BesselJ{\nu}@{x} = \frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\sin@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}</math>]] || <code>BesselJ(nu, x) = (2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((sin(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity)</code> || <code>BesselJ[\[Nu], x] == Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Sin[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None]</code> || Successful || Aborted || - || Successful [Tested: 15]
 |-
-| [https://dlmf.nist.gov/10.9#Ex6 10.9#Ex6] || [[Item:Q3080|<math>\BesselY{\nu}@{x} = -\frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}</math>]] || <code>BesselY(nu, x) = -(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((cos(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity)</code> || <code>BesselY[\[Nu], x] == -Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Cos[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None]</code> || Successful || Error || - || Skip - No test values generated
+| [https://dlmf.nist.gov/10.9#Ex6 10.9#Ex6] || [[Item:Q3080|<math>\BesselY{\nu}@{x} = -\frac{2(\tfrac{1}{2}x)^{-\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\tfrac{1}{2}-\nu}}\int_{1}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}-1)^{\nu+\frac{1}{2}}}</math>]] || <code>BesselY(nu, x) = -(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((cos(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity)</code> || <code>BesselY[\[Nu], x] == -Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Cos[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}, GenerateConditions->None]</code> || Successful || Aborted || - || Skip - No test values generated
+|-
+| [https://dlmf.nist.gov/10.9.E13 10.9.E13] || [[Item:Q3081|<math>\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\BesselJ{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos@@{\theta}}\cos@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-\zeta\cosh@@{t}-z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>((z + zeta)/(z - zeta))^((1)/(2)*nu)* BesselJ(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = (1)/(Pi)*int(exp(zeta*cos(theta))*cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- zeta*cosh(t)- z*sinh(t)- nu*t), t = 0..infinity)</code> || <code>(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]*\[Nu])* BesselJ[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == Divide[1,Pi]*Integrate[Exp[\[Zeta]*Cos[\[Theta]]]*Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- \[Zeta]*Cosh[t]- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9.E14 10.9.E14] || [[Item:Q3082|<math>\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\BesselY{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos@@{\theta}}\sin@{z\sin@@{\theta}-\nu\theta}\diff{\theta}-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t+\zeta\cosh@@{t}}+e^{-\nu t-\zeta\cosh@@{t}}\cos@{\nu\pi}\right)\*e^{-z\sinh@@{t}}\diff{t}</math>]] || <code>((z + zeta)/(z - zeta))^((1)/(2)*nu)* BesselY(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = (1)/(Pi)*int(exp(zeta*cos(theta))*sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t + zeta*cosh(t))+ exp(- nu*t - zeta*cosh(t))*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity)</code> || <code>(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]*\[Nu])* BesselY[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == Divide[1,Pi]*Integrate[Exp[\[Zeta]*Cos[\[Theta]]]*Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t + \[Zeta]*Cosh[t]]+ Exp[- \[Nu]*t - \[Zeta]*Cosh[t]]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9.E15 10.9.E15] || [[Item:Q3083|<math>\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\HankelH{1}{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = \frac{1}{\pi i}e^{-\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{iz\cosh@@{t}+i\zeta\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>((z + zeta)/(z - zeta))^((1)/(2)*nu)* HankelH1(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = (1)/(Pi*I)*exp(-(1)/(2)*nu*Pi*I)*int(exp(I*z*cosh(t)+ I*zeta*sinh(t)- nu*t), t = - infinity..infinity)</code> || <code>(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]*\[Nu])* HankelH1[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == Divide[1,Pi*I]*Exp[-Divide[1,2]*\[Nu]*Pi*I]*Integrate[Exp[I*z*Cosh[t]+ I*\[Zeta]*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9.E16 10.9.E16] || [[Item:Q3084|<math>\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}\HankelH{2}{\nu}@{(z^{2}-\zeta^{2})^{\frac{1}{2}}} = -\frac{1}{\pi i}e^{\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh@@{t}-i\zeta\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>((z + zeta)/(z - zeta))^((1)/(2)*nu)* HankelH2(nu, ((z)^(2)- (zeta)^(2))^((1)/(2))) = -(1)/(Pi*I)*exp((1)/(2)*nu*Pi*I)*int(exp(- I*z*cosh(t)- I*zeta*sinh(t)- nu*t), t = - infinity..infinity)</code> || <code>(Divide[z + \[Zeta],z - \[Zeta]])^(Divide[1,2]*\[Nu])* HankelH2[\[Nu], ((z)^(2)- \[Zeta]^(2))^(Divide[1,2])] == -Divide[1,Pi*I]*Exp[Divide[1,2]*\[Nu]*Pi*I]*Integrate[Exp[- I*z*Cosh[t]- I*\[Zeta]*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.9.E17 10.9.E17] || [[Item:Q3085|<math>\BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-\pi i}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>BesselJ(nu, z) = (1)/(2*Pi*I)*int(exp(z*sinh(t)- nu*t), t = infinity - Pi*I..infinity + Pi*I)</code> || <code>BesselJ[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, Infinity - Pi*I, Infinity + Pi*I}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[0.4358908643715884, -0.07192294931339177] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.0679098760861825, 0.09257666026367889] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.9#Ex7 10.9#Ex7] || [[Item:Q3086|<math>\HankelH{1}{\nu}@{z} = \frac{1}{\pi i}\int_{-\infty}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>HankelH1(nu, z) = (1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity + Pi*I)</code> || <code>HankelH1[\[Nu], z] == Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity + Pi*I}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9#Ex7 10.9#Ex7] || [[Item:Q3086|<math>\HankelH{1}{\nu}@{z} = \frac{1}{\pi i}\int_{-\infty}^{\infty+\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>HankelH1(nu, z) = (1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity + Pi*I)</code> || <code>HankelH1[\[Nu], z] == Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity + Pi*I}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9#Ex8 10.9#Ex8] || [[Item:Q3087|<math>\HankelH{2}{\nu}@{z} = -\frac{1}{\pi i}\int_{-\infty}^{\infty-\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>HankelH2(nu, z) = -(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity - Pi*I)</code> || <code>HankelH2[\[Nu], z] == -Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity - Pi*I}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9#Ex8 10.9#Ex8] || [[Item:Q3087|<math>\HankelH{2}{\nu}@{z} = -\frac{1}{\pi i}\int_{-\infty}^{\infty-\pi i}e^{z\sinh@@{t}-\nu t}\diff{t}</math>]] || <code>HankelH2(nu, z) = -(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity - Pi*I)</code> || <code>HankelH2[\[Nu], z] == -Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity - Pi*I}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.9.E19 10.9.E19] || [[Item:Q3088|<math>\BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}}{2\pi i}\int_{-\infty}^{(0+)}\exp@{t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}</math>]] || <code>BesselJ(nu, z) = (((1)/(2)*z)^(nu))/(2*Pi*I)*int(exp(t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = - infinity..(0 +))</code> || <code>BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],2*Pi*I]*Integrate[Exp[t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, - Infinity, (0 +)}, GenerateConditions->None]</code> || Error || Failure || - || Error
@@ Line 130: / Line 144: @@
 |-
 | [https://dlmf.nist.gov/10.9#Ex10 10.9#Ex10] || [[Item:Q3091|<math>\HankelH{2}{\nu}@{z} = \frac{\EulerGamma@{\tfrac{1}{2}-\nu}(\tfrac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1-i\infty}^{(1+)}e^{-izt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}</math>]] || <code>HankelH2(nu, z) = (GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(- I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 - I*infinity..(1 +))</code> || <code>HankelH2[\[Nu], z] == Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[3,2])* I]*Integrate[Exp[- I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 - I*Infinity, (1 +)}, GenerateConditions->None]</code> || Error || Failure || - || Error
+|-
+| [https://dlmf.nist.gov/10.9.E22 10.9.E22] || [[Item:Q3092|<math>\BesselJ{\nu}@{x} = \frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\EulerGamma@{-t}(\tfrac{1}{2}x)^{\nu+2t}}{\EulerGamma@{\nu+t+1}}\diff{t}</math>]] || <code>BesselJ(nu, x) = (1)/(2*Pi*I)*int((GAMMA(- t)*((1)/(2)*x)^(nu + 2*t))/(GAMMA(nu + t + 1)), t = - I*infinity..I*infinity)</code> || <code>BesselJ[\[Nu], x] == Divide[1,2*Pi*I]*Integrate[Divide[Gamma[- t]*(Divide[1,2]*x)^(\[Nu]+ 2*t),Gamma[\[Nu]+ t + 1]], {t, - I*Infinity, I*Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.9.E23 10.9.E23] || [[Item:Q3093|<math>\BesselJ{\nu}@{z} = \frac{1}{2\pi i}\int_{-\infty-ic}^{-\infty+ic}\frac{\EulerGamma@{t}}{\EulerGamma@{\nu-t+1}}(\tfrac{1}{2}z)^{\nu-2t}\diff{t}</math>]] || <code>BesselJ(nu, z) = (1)/(2*Pi*I)*int((GAMMA(t))/(GAMMA(nu - t + 1))*((1)/(2)*z)^(nu - 2*t), t = - infinity - I*c..- infinity + I*c)</code> || <code>BesselJ[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Divide[Gamma[t],Gamma[\[Nu]- t + 1]]*(Divide[1,2]*z)^(\[Nu]- 2*t), {t, - Infinity - I*c, - Infinity + I*c}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.4358908643715884, -0.07192294931339177] <- {Rule[c, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.0679098760861825, 0.09257666026367889] <- {Rule[c, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.9.E24 10.9.E24] || [[Item:Q3094|<math>\HankelH{1}{\nu}@{z} = -\frac{e^{-\frac{1}{2}\nu\pi i}}{2\pi^{2}}\*\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(-\tfrac{1}{2}iz)^{\nu-2t}\diff{t}</math>]] || <code>HankelH1(nu, z) = -(exp(-(1)/(2)*nu*Pi*I))/(2*(Pi)^(2))* int(GAMMA(t)*GAMMA(t - nu)*(-(1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>HankelH1[\[Nu], z] == -Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]* Integrate[Gamma[t]*Gamma[t - \[Nu]]*(-Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 120]<div class="mw-collapsible-content"><code>120/120]: [[.2971181619-.8401954886*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.8661908042+.2691615148*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E24 10.9.E24] || [[Item:Q3094|<math>\HankelH{1}{\nu}@{z} = -\frac{e^{-\frac{1}{2}\nu\pi i}}{2\pi^{2}}\*\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(-\tfrac{1}{2}iz)^{\nu-2t}\diff{t}</math>]] || <code>HankelH1(nu, z) = -(exp(-(1)/(2)*nu*Pi*I))/(2*(Pi)^(2))* int(GAMMA(t)*GAMMA(t - nu)*(-(1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>HankelH1[\[Nu], z] == -Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]* Integrate[Gamma[t]*Gamma[t - \[Nu]]*(-Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 120]<div class="mw-collapsible-content"><code>120/120]: [[.2971181619-.8401954886*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.8661908042+.2691615148*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9.E25 10.9.E25] || [[Item:Q3095|<math>\HankelH{2}{\nu}@{z} = \frac{e^{\frac{1}{2}\nu\pi i}}{2\pi^{2}}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}iz)^{\nu-2t}\diff{t}</math>]] || <code>HankelH2(nu, z) = (exp((1)/(2)*nu*Pi*I))/(2*(Pi)^(2))*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>HankelH2[\[Nu], z] == Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 120]<div class="mw-collapsible-content"><code>120/120]: [[-.1414870617+.1246394392*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>-.1498748781e-1-.1846515642*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br></div></div> || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E25 10.9.E25] || [[Item:Q3095|<math>\HankelH{2}{\nu}@{z} = \frac{e^{\frac{1}{2}\nu\pi i}}{2\pi^{2}}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}iz)^{\nu-2t}\diff{t}</math>]] || <code>HankelH2(nu, z) = (exp((1)/(2)*nu*Pi*I))/(2*(Pi)^(2))*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>HankelH2[\[Nu], z] == Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 120]<div class="mw-collapsible-content"><code>120/120]: [[-.1414870617+.1246394392*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>-.1498748781e-1-.1846515642*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br></div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9.E26 10.9.E26] || [[Item:Q3096|<math>\BesselJ{\mu}@{z}\BesselJ{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</math>]] || <code>BesselJ(mu, z)*BesselJ(nu, z) = (2)/(Pi)*int(BesselJ(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..Pi/ 2)</code> || <code>BesselJ[\[Mu], z]*BesselJ[\[Nu], z] == Divide[2,Pi]*Integrate[BesselJ[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None]</code> || Failure || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E26 10.9.E26] || [[Item:Q3096|<math>\BesselJ{\mu}@{z}\BesselJ{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</math>]] || <code>BesselJ(mu, z)*BesselJ(nu, z) = (2)/(Pi)*int(BesselJ(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..Pi/ 2)</code> || <code>BesselJ[\[Mu], z]*BesselJ[\[Nu], z] == Divide[2,Pi]*Integrate[BesselJ[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None]</code> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.9.E27 10.9.E27] || [[Item:Q3097|<math>\BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{2\nu}@{2(z\zeta)^{\frac{1}{2}}\sin@@{\theta}}\cos@{(z-\zeta)\cos@@{\theta}}\diff{\theta}</math>]] || <code>BesselJ(nu, z)*BesselJ(nu, zeta) = (2)/(Pi)*int(BesselJ(2*nu, 2*(z*zeta)^((1)/(2))* sin(theta))*cos((z - zeta)* cos(theta)), theta = 0..Pi/ 2)</code> || <code>BesselJ[\[Nu], z]*BesselJ[\[Nu], \[Zeta]] == Divide[2,Pi]*Integrate[BesselJ[2*\[Nu], 2*(z*\[Zeta])^(Divide[1,2])* Sin[\[Theta]]]*Cos[(z - \[Zeta])* Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None]</code> || Failure || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E27 10.9.E27] || [[Item:Q3097|<math>\BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{2}{\pi}\int_{0}^{\pi/2}\BesselJ{2\nu}@{2(z\zeta)^{\frac{1}{2}}\sin@@{\theta}}\cos@{(z-\zeta)\cos@@{\theta}}\diff{\theta}</math>]] || <code>BesselJ(nu, z)*BesselJ(nu, zeta) = (2)/(Pi)*int(BesselJ(2*nu, 2*(z*zeta)^((1)/(2))* sin(theta))*cos((z - zeta)* cos(theta)), theta = 0..Pi/ 2)</code> || <code>BesselJ[\[Nu], z]*BesselJ[\[Nu], \[Zeta]] == Divide[2,Pi]*Integrate[BesselJ[2*\[Nu], 2*(z*\[Zeta])^(Divide[1,2])* Sin[\[Theta]]]*Cos[(z - \[Zeta])* Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}, GenerateConditions->None]</code> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.9.E28 10.9.E28] || [[Item:Q3098|<math>\BesselJ{\nu}@{z}\BesselJ{\nu}@{\zeta} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp@{\frac{1}{2}t-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselI{\nu}@{\frac{z\zeta}{t}}\frac{\diff{t}}{t}</math>]] || <code>BesselJ(nu, z)*BesselJ(nu, zeta) = (1)/(2*Pi*I)*int(* exp((1)/(2)*t -((z)^(2)+ (zeta)^(2))/(2*t))*BesselI(nu, (z*zeta)/(t))*(1)/(t), t = c - I*infinity..c + I*infinity)</code> || <code>BesselJ[\[Nu], z]*BesselJ[\[Nu], \[Zeta]] == Divide[1,2*Pi*I]*Integrate[* Exp[Divide[1,2]*t -Divide[(z)^(2)+ \[Zeta]^(2),2*t]]*BesselI[\[Nu], Divide[z*\[Zeta],t]]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/10.9.E30 10.9.E30] || [[Item:Q3100|<math>\BesselJ{\nu}^{2}@{z}+\BesselY{\nu}^{2}@{z} = \frac{8}{\pi^{2}}\int_{0}^{\infty}\cosh@{2\nu t}\modBesselK{0}@{2z\sinh@@{t}}\diff{t}</math>]] || <code>(BesselJ(nu, z))^(2)+ (BesselY(nu, z))^(2) = (8)/((Pi)^(2))*int(cosh(2*nu*t)*BesselK(0, 2*z*sinh(t)), t = 0..infinity)</code> || <code>(BesselJ[\[Nu], z])^(2)+ (BesselY[\[Nu], z])^(2) == Divide[8,(Pi)^(2)]*Integrate[Cosh[2*\[Nu]*t]*BesselK[0, 2*z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.9.E29 10.9.E29] || [[Item:Q3099|<math>\BesselJ{\mu}@{x}\BesselJ{\nu}@{x} = \frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\EulerGamma@{-t}\EulerGamma@{2t+\mu+\nu+1}(\tfrac{1}{2}x)^{\mu+\nu+2t}}{\EulerGamma@{t+\mu+1}\EulerGamma@{t+\nu+1}\EulerGamma@{t+\mu+\nu+1}}\diff{t}</math>]] || <code>BesselJ(mu, x)*BesselJ(nu, x) = (1)/(2*Pi*I)*int((GAMMA(- t)*GAMMA(2*t + mu + nu + 1)*((1)/(2)*x)^(mu + nu + 2*t))/(GAMMA(t + mu + 1)*GAMMA(t + nu + 1)*GAMMA(t + mu + nu + 1)), t = - I*infinity..I*infinity)</code> || <code>BesselJ[\[Mu], x]*BesselJ[\[Nu], x] == Divide[1,2*Pi*I]*Integrate[Divide[Gamma[- t]*Gamma[2*t + \[Mu]+ \[Nu]+ 1]*(Divide[1,2]*x)^(\[Mu]+ \[Nu]+ 2*t),Gamma[t + \[Mu]+ 1]*Gamma[t + \[Nu]+ 1]*Gamma[t + \[Mu]+ \[Nu]+ 1]], {t, - I*Infinity, I*Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.9.E30 10.9.E30] || [[Item:Q3100|<math>\BesselJ{\nu}^{2}@{z}+\BesselY{\nu}^{2}@{z} = \frac{8}{\pi^{2}}\int_{0}^{\infty}\cosh@{2\nu t}\modBesselK{0}@{2z\sinh@@{t}}\diff{t}</math>]] || <code>(BesselJ(nu, z))^(2)+ (BesselY(nu, z))^(2) = (8)/((Pi)^(2))*int(cosh(2*nu*t)*BesselK(0, 2*z*sinh(t)), t = 0..infinity)</code> || <code>(BesselJ[\[Nu], z])^(2)+ (BesselY[\[Nu], z])^(2) == Divide[8,(Pi)^(2)]*Integrate[Cosh[2*\[Nu]*t]*BesselK[0, 2*z*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.11.E1 10.11.E1] || [[Item:Q3103|<math>\BesselJ{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\BesselJ{\nu}@{z}</math>]] || <code>BesselJ(nu, z*exp(m*Pi*I)) = exp(m*nu*Pi*I)*BesselJ(nu, z)</code> || <code>BesselJ[\[Nu], z*Exp[m*Pi*I]] == Exp[m*\[Nu]*Pi*I]*BesselJ[\[Nu], z]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [132 / 210]<div class="mw-collapsible-content"><code>132/210]: [[-1.978604450-.5916012221*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</code><br><code>.4256613630-.5580360922e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.9786044502778974, -0.5916012230349773] <- {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.42566136315461117, -0.05580360945599949] <- {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
@@ Line 175: / Line 193: @@
 | [https://dlmf.nist.gov/10.12#Ex1 10.12#Ex1] || [[Item:Q3117|<math>\cos@{z\sin@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}\BesselJ{2k}@{z}\cos@{2k\theta}</math>]] || <code>cos(z*sin(theta)) = BesselJ(0, z)+ 2*sum(BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity)</code> || <code>Cos[z*Sin[\[Theta]]] == BesselJ[0, z]+ 2*Sum[BesselJ[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Successful || Skipped - Because timed out || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/10.12#Ex2 10.12#Ex2] || [[Item:Q3118|<math>\sin@{z\sin@@{\theta}} = 2\sum_{k=0}^{\infty}\BesselJ{2k+1}@{z}\sin@{(2k+1)\theta}</math>]] || <code>sin(z*sin(theta)) = 2*sum(BesselJ(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity)</code> || <code>Sin[z*Sin[\[Theta]]] == 2*Sum[BesselJ[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Successful || Skipped - Because timed out || Successful [Tested: 70]
+| [https://dlmf.nist.gov/10.12#Ex2 10.12#Ex2] || [[Item:Q3118|<math>\sin@{z\sin@@{\theta}} = 2\sum_{k=0}^{\infty}\BesselJ{2k+1}@{z}\sin@{(2k+1)\theta}</math>]] || <code>sin(z*sin(theta)) = 2*sum(BesselJ(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity)</code> || <code>Sin[z*Sin[\[Theta]]] == 2*Sum[BesselJ[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Successful || Skipped - Because timed out || Successful [Tested: 70]
 |-
 | [https://dlmf.nist.gov/10.12#Ex3 10.12#Ex3] || [[Item:Q3119|<math>\cos@{z\cos@@{\theta}} = \BesselJ{0}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{2k}@{z}\cos@{2k\theta}</math>]] || <code>cos(z*cos(theta)) = BesselJ(0, z)+ 2*sum((- 1)^(k)* BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity)</code> || <code>Cos[z*Cos[\[Theta]]] == BesselJ[0, z]+ 2*Sum[(- 1)^(k)* BesselJ[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Successful || Skipped - Because timed out || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/10.12#Ex4 10.12#Ex4] || [[Item:Q3120|<math>\sin@{z\cos@@{\theta}} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{2k+1}@{z}\cos@{(2k+1)\theta}</math>]] || <code>sin(z*cos(theta)) = 2*sum((- 1)^(k)* BesselJ(2*k + 1, z)*cos((2*k + 1)* theta), k = 0..infinity)</code> || <code>Sin[z*Cos[\[Theta]]] == 2*Sum[(- 1)^(k)* BesselJ[2*k + 1, z]*Cos[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Successful || Skipped - Because timed out || Successful [Tested: 70]
+| [https://dlmf.nist.gov/10.12#Ex4 10.12#Ex4] || [[Item:Q3120|<math>\sin@{z\cos@@{\theta}} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{2k+1}@{z}\cos@{(2k+1)\theta}</math>]] || <code>sin(z*cos(theta)) = 2*sum((- 1)^(k)* BesselJ(2*k + 1, z)*cos((2*k + 1)* theta), k = 0..infinity)</code> || <code>Sin[z*Cos[\[Theta]]] == 2*Sum[(- 1)^(k)* BesselJ[2*k + 1, z]*Cos[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Successful || Skipped - Because timed out || Successful [Tested: 70]
 |-
 | [https://dlmf.nist.gov/10.12.E4 10.12.E4] || [[Item:Q3121|<math>1 = \BesselJ{0}@{z}+2\BesselJ{2}@{z}+2\BesselJ{4}@{z}+2\BesselJ{6}@{z}+\dotsb</math>]] || <code>1 = BesselJ(0, z)+ 2*BesselJ(2, z)+ 2*BesselJ(4, z)+ 2*BesselJ(6, z)+ ..</code> || <code>1 == BesselJ[0, z]+ 2*BesselJ[2, z]+ 2*BesselJ[4, z]+ 2*BesselJ[6, z]+ \[Ellipsis]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[-9.924736618779559*^-8, -1.6360842739013975*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-9.440290587615918*^-8, -1.7199789187696823*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 241: / Line 259: @@
 | [https://dlmf.nist.gov/10.16#Ex4 10.16#Ex4] || [[Item:Q3159|<math>i\HankelH{2}{-\frac{1}{2}}@{z} = i\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}e^{-iz}</math>]] || <code>I*HankelH2(-(1)/(2), z) = I*((2)/(Pi*z))^((1)/(2))* exp(- I*z)</code> || <code>I*HankelH2[-Divide[1,2], z] == I*(Divide[2,Pi*z])^(Divide[1,2])* Exp[- I*z]</code> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.16#Ex5 10.16#Ex5] || [[Item:Q3160|<math>\BesselJ{\frac{1}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(\paraW@{0}{2z^{\frac{1}{2}}}-\paraW@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[Divide[1,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[1,4])*(Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] )- Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), - 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), - 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] ))</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.8427727646508262, -0.04212015747529019], Times[Complex[0.4703662267003617, -0.06192488852586185], Plus[Times[0.4550898605622274, Plus[Times[Complex[0.3150667711363517, -1.1318933470332309], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.1941072423227021, 0.35884759380625464], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[1.684848183162187, 0.4798071226199044], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.8058077119758371, -1.0109338182195815], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.7942814592773979, 0.6544287188687908], Times[Complex[0.41086410074312574, -0.23721249916439713], Plus[Times[0.4550898605622274, Plus[Times[Complex[1.9382359752879499, -0.7976721648462198], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.22978077998995444, -0.1584303699393873], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[0.8690225748967872, 1.5500248253586082], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[2.5774777701947826, 0.910783030451775], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.16#Ex5 10.16#Ex5] || [[Item:Q3160|<math>\BesselJ{\frac{1}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(\paraW@{0}{2z^{\frac{1}{2}}}-\paraW@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[Divide[1,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[1,4])*(Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] )- Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), - 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), - 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] ))</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.8427727646508262, -0.04212015747529019], Times[Complex[0.4703662267003617, -0.06192488852586185], Plus[Times[0.4550898605622274, Plus[Times[Complex[0.3150667711363517, -1.1318933470332309], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.1941072423227021, 0.35884759380625464], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[1.684848183162187, 0.4798071226199044], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.8058077119758371, -1.0109338182195815], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.7942814592773979, 0.6544287188687908], Times[Complex[</div></div>
+|-
+| [https://dlmf.nist.gov/10.16#Ex6 10.16#Ex6] || [[Item:Q3161|<math>\BesselJ{-\frac{1}{4}}@{z} = 2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{1}{4}}\left(\paraW@{0}{2z^{\frac{1}{2}}}+\paraW@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[-Divide[1,4], z] == (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[1,4])*(Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] )+ Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), - 2*(z)^(Divide[1,2]) * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), - 2*(z)^(Divide[1,2]) * Exp[Divide[Pi*I,4]]] ))</code> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.7570692040611657, -0.36205959587261455], Times[Complex[-0.4703662267003617, 0.06192488852586186], Plus[Times[0.4550898605622274, Plus[Times[Complex[0.3150667711363517, -1.1318933470332309], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[0.1941072423227021, 0.35884759380625464], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[1.684848183162187, 0.4798071226199044], Power[2.718281828459045, Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]], Times[Complex[1.8058077119758371, -1.0109338182195815], Power[2.718281828459045, Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[1.1199640481676587, -0.30003362129733535], Times[Complex</div></div>
 |-
-| [https://dlmf.nist.gov/10.16#Ex7 10.16#Ex7] || [[Item:Q3162|<math>\BesselJ{\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}-\paraW'@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])*((D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 2*(z)^(Divide[1,2]))- (D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> - 2*(z)^(Divide[1,2])))</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5824093961234496, 0.15854248220296385], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.0836786417162193, 0.6909849218136797], Times[Complex[0.0, -0.4744249983287943], Plus[Times[-0.4550898605622274, Plus[Times[Complex[-1.52733809531001, -0.015580244977093649], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-1.3790215645615536, -1.2403191305633965], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[-0.154282678975249, -1.0920025998149403], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.302599209723706, 0.13273628577136276], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.16#Ex7 10.16#Ex7] || [[Item:Q3162|<math>\BesselJ{\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}-\paraW'@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])*((D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 2*(z)^(Divide[1,2]))- (D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> - 2*(z)^(Divide[1,2])))</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5824093961234496, 0.15854248220296385], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[-0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAM</div></div>
 |-
-| [https://dlmf.nist.gov/10.16#Ex8 10.16#Ex8] || [[Item:Q3163|<math>\BesselJ{-\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}+\paraW'@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[-Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])*((D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 2*(z)^(Divide[1,2]))+ (D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> - 2*(z)^(Divide[1,2])))</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.05605283808026881, -0.4145839244466886], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.44186162583484034, -0.6708696264637843], Times[Complex[0.0, -0.4744249983287943], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.52733809531001, -0.015580244977093649], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-1.3790215645615536, -1.2403191305633965], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[-0.154282678975249, -1.0920025998149403], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.302599209723706, 0.13273628577136276], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]]]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.16#Ex8 10.16#Ex8] || [[Item:Q3163|<math>\BesselJ{-\frac{3}{4}}@{z} = -2^{-\frac{1}{4}}\pi^{-\frac{1}{2}}z^{-\frac{3}{4}}\left(\paraW'@{0}{2z^{\frac{1}{2}}}+\paraW'@{0}{-2z^{\frac{1}{2}}}\right)</math>]] || <code>Error</code> || <code>BesselJ[-Divide[3,4], z] == - (2)^(-Divide[1,4])* (Pi)^(-Divide[1,2])* (z)^(-Divide[3,4])*((D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> 2*(z)^(Divide[1,2]))+ (D[Sqrt[(Sqrt[1+Exp[2*Pi*(0)]]-Exp[Pi*(0)])/2] * Exp[Divide[Pi*(0),4]] * ( Exp[I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 - I*(0), temp * Exp[-Divide[Pi*I,4]]] + Exp[-I*(Pi/8 + Arg[GAMMA[1/2 + I*(0)]]/2)] * ParabolicCylinderD[- 1/2 + I*(0), temp * Exp[Divide[Pi*I,4]]] ), {temp, 1}]/.temp-> - 2*(z)^(Divide[1,2])))</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.05605283808026881, -0.4145839244466886], Times[Complex[0.43831154566767444, -0.18155458676026498], Plus[Times[0.4550898605622274, Plus[Times[Complex[-1.0141669743850696, 0.548925751618472], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.3595065696883391, -0.29725176260213915], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]]]], Times[0.4550898605622274, Plus[Times[Complex[0.48667094453227255, 0.3574086420945919], Power[2.718281828459045, Plus[Complex[0.0, 0.7853981633974483], Times[Complex[0.0, -1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAMMA[0.5]]]]]]]], Times[Complex[-0.16798946016445826, 1.2035861563152026], Power[2.718281828459045, Plus[Complex[0.0, -0.7853981633974483], Times[Complex[0.0, 1.0], Plus[0.39269908169872414, Times[0.5, Arg[GAM</div></div>
 |-
 | [https://dlmf.nist.gov/10.16.E5 10.16.E5] || [[Item:Q3164|<math>\BesselJ{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- iz}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2iz}</math>]] || <code>BesselJ(nu, z) = (((1)/(2)*z)^(nu)* exp(- I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, + 2*I*z)</code> || <code>BesselJ[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu]* Exp[- I*z],Gamma[\[Nu]+ 1]]*Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, + 2*I*z]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 56]<div class="mw-collapsible-content"><code>7/56]: [[-.827986137e-1+.7317301038*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.8060140108+.3257248263*I <- {nu = -1/2, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 56]<div class="mw-collapsible-content"><code>{Complex[-0.08279861346468581, 0.7317301035002939] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}</code><br><code>Complex[-0.8060140105131326, 0.32572482654389856] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]}</code><br></div></div>
@@ Line 259: / Line 279: @@
 | [https://dlmf.nist.gov/10.17.E7 10.17.E7] || [[Item:Q3176|<math>z^{\frac{1}{2}} = \exp@{\tfrac{1}{2}\ln@@{|z|}+\tfrac{1}{2}i\phase@@{z}}</math>]] || <code>(z)^((1)/(2)) = exp((1)/(2)*ln(abs(z))+(1)/(2)*I*argument(z))</code> || <code>(z)^(Divide[1,2]) == Exp[Divide[1,2]*Log[Abs[z]]+Divide[1,2]*I*Arg[z]]</code> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.17.E16 10.17.E16] || [[Item:Q3185|<math>\scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}</math>]] || <code>(exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z) = (exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z)</code> || <code>Error</code> || Successful || Error || - || -
+| [https://dlmf.nist.gov/10.17.E16 10.17.E16] || [[Item:Q3185|<math>\scterminant{p}@{z} = \frac{e^{z}}{2\pi}\EulerGamma@{p}\incGamma@{1-p}{z}</math>]] || <code>(exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z) = (exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z)</code> || <code>Error</code> || Successful || Missing Macro Error || - || -
+|-
+| [https://dlmf.nist.gov/10.17.E17 10.17.E17] || [[Item:Q3186|<math>R_{\ell}^{+}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(+ i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{- 2iz}+R_{m,\ell}^{+}(\nu,z)\right)</math>]] || <code>(R[ell])^(+)*(nu , z) = (- 1)^(ell)* 2*cos(nu*Pi)(sum((+ I)^(k)*(a[k]*(nu))/((z)^(k))*(exp(- 2*I*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,- 2*I*z), k = 0..m - 1)+ R(R[m , ell])^(+)*(nu , z))</code> || <code>Error</code> || Error || Missing Macro Error || - || -
 |-
-| [https://dlmf.nist.gov/10.18#Ex7 10.18#Ex7] || [[Item:Q3196|<math>\HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((BesselJ[\[Nu], x])^(2)+ (BesselY[\[Nu], x])^(2))^(Divide[1,2])</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[0.19554332981034928, -0.3390785475644471] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.7197518351343698, 1.0182547128018542] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.17.E17 10.17.E17] || [[Item:Q3186|<math>R_{\ell}^{-}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}(- i)^{k}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{+ 2iz}+R_{m,\ell}^{-}(\nu,z)\right)</math>]] || <code>(R[ell])^(-)*(nu , z) = (- 1)^(ell)* 2*cos(nu*Pi)(sum((- I)^(k)*(a[k]*(nu))/((z)^(k))*(exp(+ 2*I*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,+ 2*I*z), k = 0..m - 1)+ R(R[m , ell])^(-)*(nu , z))</code> || <code>Error</code> || Error || Missing Macro Error || - || -
 |-
-| [https://dlmf.nist.gov/10.18#Ex8 10.18#Ex8] || [[Item:Q3197|<math>\HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((D[BesselJ[\[Nu], x], {x, 1}])^(2)+ (D[BesselY[\[Nu], x], {x, 1}])^(2))^(Divide[1,2])</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[-0.3065654786420606, 0.09106250304027241] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.41179972752410343, -0.08651542233456301] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.18#Ex7 10.18#Ex7] || [[Item:Q3196|<math>\HankelmodM{\nu}@{x} = \left(\BesselJ{\nu}^{2}@{x}+\BesselY{\nu}^{2}@{x}\right)^{\frac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((BesselJ[\[Nu], x])^(2)+ (BesselY[\[Nu], x])^(2))^(Divide[1,2])</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[0.19554332981034928, -0.3390785475644471] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.7197518351343698, 1.0182547128018542] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.18#Ex8 10.18#Ex8] || [[Item:Q3197|<math>\HankelmodderivN{\nu}@{x} = \left(\BesselJ{\nu}'^{2}@{x}+\BesselY{\nu}'^{2}@{x}\right)^{\frac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((D[BesselJ[\[Nu], x], {x, 1}])^(2)+ (D[BesselY[\[Nu], x], {x, 1}])^(2))^(Divide[1,2])</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[-0.3065654786420606, 0.09106250304027241] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.41179972752410343, -0.08651542233456301] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.18.E10 10.18.E10] || [[Item:Q3203|<math>(x^{2}-\nu^{2})\HankelmodM{\nu}@{x}\HankelmodM{\nu}'@{x}+x^{2}\HankelmodderivN{\nu}@{x}\HankelmodderivN{\nu}'@{x}+x\HankelmodderivN{\nu}^{2}@{x} = 0</math>]] || <code>Error</code> || <code>((x)^(2)- \[Nu]^(2))* Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2]*D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 1}]+ (x)^(2)* Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]*D[Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2], {x, 1}]+ x*(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2) == 0</code> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[0.7620133104065328, -0.7345190431210711] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-3.2607567755462643, -4.475082123070706] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.18.E13 10.18.E13] || [[Item:Q3206|<math>x^{2}\HankelmodM{\nu}''@{x}+x\HankelmodM{\nu}'@{x}+(x^{2}-\nu^{2})\HankelmodM{\nu}@{x} = \frac{4}{\pi^{2}{\HankelmodM{\nu}^{3}(x)}}</math>]] || <code>Error</code> || <code>(x)^(2)* D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 2}]+ x*D[Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2], {x, 1}]+((x)^(2)- \[Nu]^(2))* Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == Divide[4,(Pi)^(2)*(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(3)]</code> || Missing Macro Error || Translation Error || - || -
 |-
 | [https://dlmf.nist.gov/10.20.E1 10.20.E1] || [[Item:Q3250|<math>\left(\deriv{\zeta}{z}\right)^{2} = \frac{1-z^{2}}{\zeta z^{2}}</math>]] || <code>(diff(zeta, z))^(2) = (1 - (z)^(2))/(zeta*(z)^(2))</code> || <code>(D[\[Zeta], z])^(2) == Divide[1 - (z)^(2),\[Zeta]*(z)^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>70/70]: [[.8660254030+.4999999994*I <- {z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}</code><br><code>.4999999994-.8660254030*I <- {z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[0.8660254037844386, 0.4999999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4999999999999999, -0.8660254037844386] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.20.E3 10.20.E3] || [[Item:Q3252|<math>\frac{2}{3}(-\zeta)^{\frac{3}{2}} = \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t}</math>]] || <code>(2)/(3)*(- zeta)^((3)/(2)) = int((sqrt((t)^(2)- 1))/(t), t = 1..z)</code> || <code>Divide[2,3]*(- \[Zeta])^(Divide[3,2]) == Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 20]<div class="mw-collapsible-content"><code>20/20]: [[-.7483698391+.4714045210*I <- {z = 3/2, zeta = 1/2*3^(1/2)+1/2*I}</code><br><code>-.2769653183-.6666666667*I <- {z = 3/2, zeta = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 20]<div class="mw-collapsible-content"><code>{Complex[-0.7483698389729962, 0.4714045207910317] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.27696531818196457, -0.6666666666666666] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.20.E2 10.20.E2] || [[Item:Q3251|<math>\frac{2}{3}\zeta^{\frac{3}{2}} = \int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t}</math>]] || <code>(2)/(3)*(zeta)^((3)/(2)) = int((sqrt(1 - (t)^(2)))/(t), t = z..1)</code> || <code>Divide[2,3]*\[Zeta]^(Divide[3,2]) == Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.20.E2 10.20.E2] || [[Item:Q3251|<math>\int_{z}^{1}\frac{\sqrt{1-t^{2}}}{t}\diff{t} = \ln@{\frac{1+\sqrt{1-z^{2}}}{z}}-\sqrt{1-z^{2}}</math>]] || <code>int((sqrt(1 - (t)^(2)))/(t), t = z..1) = ln((1 +sqrt(1 - (z)^(2)))/(z))-sqrt(1 - (z)^(2))</code> || <code>Integrate[Divide[Sqrt[1 - (t)^(2)],t], {t, z, 1}, GenerateConditions->None] == Log[Divide[1 +Sqrt[1 - (z)^(2)],z]]-Sqrt[1 - (z)^(2)]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.20.E3 10.20.E3] || [[Item:Q3252|<math>\frac{2}{3}(-\zeta)^{\frac{3}{2}} = \int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t}</math>]] || <code>(2)/(3)*(- zeta)^((3)/(2)) = int((sqrt((t)^(2)- 1))/(t), t = 1..z)</code> || <code>Divide[2,3]*(- \[Zeta])^(Divide[3,2]) == Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 20]<div class="mw-collapsible-content"><code>20/20]: [[-.7483698391+.4714045210*I <- {z = 3/2, zeta = 1/2*3^(1/2)+1/2*I}</code><br><code>-.2769653183-.6666666667*I <- {z = 3/2, zeta = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 20]<div class="mw-collapsible-content"><code>{Complex[-0.7483698389729962, 0.4714045207910317] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.27696531818196457, -0.6666666666666666] <- {Rule[z, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.20.E3 10.20.E3] || [[Item:Q3252|<math>\int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t} = \sqrt{z^{2}-1}-\asec@@{z}</math>]] || <code>int((sqrt((t)^(2)- 1))/(t), t = 1..z) = sqrt((z)^(2)- 1)- arcsec(z)</code> || <code>Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None] == Sqrt[(z)^(2)- 1]- ArcSec[z]</code> || Failure || Error || Successful [Tested: 2] || Successful [Tested: 2]
+| [https://dlmf.nist.gov/10.20.E3 10.20.E3] || [[Item:Q3252|<math>\int_{1}^{z}\frac{\sqrt{t^{2}-1}}{t}\diff{t} = \sqrt{z^{2}-1}-\asec@@{z}</math>]] || <code>int((sqrt((t)^(2)- 1))/(t), t = 1..z) = sqrt((z)^(2)- 1)- arcsec(z)</code> || <code>Integrate[Divide[Sqrt[(t)^(2)- 1],t], {t, 1, z}, GenerateConditions->None] == Sqrt[(z)^(2)- 1]- ArcSec[z]</code> || Failure || Aborted || Successful [Tested: 2] || Successful [Tested: 2]
 |-
 | [https://dlmf.nist.gov/10.20#Ex1 10.20#Ex1] || [[Item:Q3263|<math>A_{0}(0) = 1</math>]] || <code>A[0]*(0) = 1</code> || <code>Subscript[A, 0]*(0) == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
@@ Line 299: / Line 331: @@
 | [https://dlmf.nist.gov/10.21.E11 10.21.E11] || [[Item:Q3292|<math>2\rho_{\nu}^{2}\deriv{\rho_{\nu}}{t}\deriv[3]{\rho_{\nu}}{t}-3\rho_{\nu}^{2}\*\left(\deriv[2]{\rho_{\nu}}{t}\right)^{2}-4\pi^{2}\rho_{\nu}^{2}\*\left(\deriv{\rho_{\nu}}{t}\right)^{2}+(4\rho_{\nu}^{2}+1-4\nu^{2})\left(\deriv{\rho_{\nu}}{t}\right)^{4} = 0</math>]] || <code>2*(rho[nu])^(2)*diff(rho[nu], t)*diff(rho[nu], [t$(3)])- 3*(rho[nu])^(2)*(diff(rho[nu], [t$(2)]))^(2)- 4*(Pi)^(2)* (rho[nu])^(2)*(diff(rho[nu], t))^(2)(4*rho(rho[nu])^(2)+ 1 - 4*(nu)^(2))*(diff(rho[nu], t))^(4) = 0</code> || <code>2*(Subscript[\[Rho], \[Nu]])^(2)*D[Subscript[\[Rho], \[Nu]], t]*D[Subscript[\[Rho], \[Nu]], {t, 3}]- 3*(Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], {t, 2}])^(2)- 4*(Pi)^(2)* (Subscript[\[Rho], \[Nu]])^(2)*(D[Subscript[\[Rho], \[Nu]], t])^(2)(4*\[Rho](Subscript[\[Rho], \[Nu]])^(2)+ 1 - 4*\[Nu]^(2))*(D[Subscript[\[Rho], \[Nu]], t])^(4) == 0</code> || Successful || Successful || - || Successful [Tested: 300]
 |-
-| [https://dlmf.nist.gov/10.21.E17 10.21.E17] || [[Item:Q3301|<math>\deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}</math>]] || <code>diff(c, nu) = 2*c*int(BesselK(0, 2*c*sinh(t))*exp(- 2*nu*t), t = 0..infinity)</code> || <code>D[c, \[Nu]] == 2*c*Integrate[BesselK[0, 2*c*Sinh[t]]*Exp[- 2*\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.21.E17 10.21.E17] || [[Item:Q3301|<math>\deriv{c}{\nu} = 2c\int_{0}^{\infty}\modBesselK{0}@{2c\sinh@@{t}}e^{-2\nu t}\diff{t}</math>]] || <code>diff(c, nu) = 2*c*int(BesselK(0, 2*c*sinh(t))*exp(- 2*nu*t), t = 0..infinity)</code> || <code>D[c, \[Nu]] == 2*c*Integrate[BesselK[0, 2*c*Sinh[t]]*Exp[- 2*\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.21#Ex19 10.21#Ex19] || [[Item:Q3309|<math>\alpha_{0} = 1</math>]] || <code>alpha[0] = 1</code> || <code>Subscript[\[Alpha], 0] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
@@ Line 341: / Line 373: @@
 | [https://dlmf.nist.gov/10.22.E10 10.22.E10] || [[Item:Q3384|<math>\int_{0}^{x}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = x^{\mu}\frac{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}}\*\sum_{k=0}^{\infty}\frac{(\nu+2k+1)\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}+k}}{\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{2}+k}}\BesselJ{\nu+2k+1}@{x}</math>]] || <code>int((t)^(mu)* BesselJ(nu, t), t = 0..x) = (x)^(mu)*(GAMMA((1)/(2)*nu +(1)/(2)*mu +(1)/(2)))/(GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)))* sum(((nu + 2*k + 1)* GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)+ k))/(GAMMA((1)/(2)*nu +(1)/(2)*mu +(3)/(2)+ k))*BesselJ(nu + 2*k + 1, x), k = 0..infinity)</code> || <code>Integrate[(t)^\[Mu]* BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == (x)^\[Mu]*Divide[Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[1,2]],Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]]* Sum[Divide[(\[Nu]+ 2*k + 1)* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]+ k],Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[3,2]+ k]]*BesselJ[\[Nu]+ 2*k + 1, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E11 10.22.E11] || [[Item:Q3385|<math>\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\BesselJ{k}@{x}</math>]] || <code>int((1 - BesselJ(0, t))/(t), t = 0..x) = (1)/(2)*sum((Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselJ(k, x), k = 1..infinity)</code> || <code>Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*Sum[Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselJ[k, x], {k, 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[0.2622772441151432, Times[-0.5, NSum[Times[Power[0.75, k], BesselJ[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}</code><br><code>Plus[0.03100698635091531, Times[-0.5, NSum[Times[Power[0.25, k], BesselJ[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.22.E11 10.22.E11] || [[Item:Q3385|<math>\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\BesselJ{k}@{x}</math>]] || <code>int((1 - BesselJ(0, t))/(t), t = 0..x) = (1)/(2)*sum((Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselJ(k, x), k = 1..infinity)</code> || <code>Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*Sum[Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselJ[k, x], {k, 1, Infinity}, GenerateConditions->None]</code> || Aborted || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[0.2622772441151432, Times[-0.5, NSum[Times[Power[0.75, k], BesselJ[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}</code><br><code>Plus[0.03100698635091531, Times[-0.5, NSum[Times[Power[0.25, k], BesselJ[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E12 10.22.E12] || [[Item:Q3386|<math>x\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = 2\sum_{k=0}^{\infty}(2k+3)(\digamma@{k+2}-\digamma@{1})\BesselJ{2k+3}@{x}</math>]] || <code>x*int((1 - BesselJ(0, t))/(t), t = 0..x) = 2*sum((2*k + 3)*(Psi(k + 2)- Psi(1))* BesselJ(2*k + 3, x), k = 0..infinity)</code> || <code>x*Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == 2*Sum[(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselJ[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 3] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E12 10.22.E12] || [[Item:Q3386|<math>x\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = 2\sum_{k=0}^{\infty}(2k+3)(\digamma@{k+2}-\digamma@{1})\BesselJ{2k+3}@{x}</math>]] || <code>x*int((1 - BesselJ(0, t))/(t), t = 0..x) = 2*sum((2*k + 3)*(Psi(k + 2)- Psi(1))* BesselJ(2*k + 3, x), k = 0..infinity)</code> || <code>x*Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == 2*Sum[(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselJ[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 3] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E12 10.22.E12] || [[Item:Q3386|<math>2\sum_{k=0}^{\infty}(2k+3)(\digamma@{k+2}-\digamma@{1})\BesselJ{2k+3}@{x} = x-2\BesselJ{1}@{x}+2\sum_{k=0}^{\infty}(2k+5)\*(\digamma@{k+3}-\digamma@{1}-1)\BesselJ{2k+5}@{x}</math>]] || <code>2*sum((2*k + 3)*(Psi(k + 2)- Psi(1))* BesselJ(2*k + 3, x), k = 0..infinity) = x - 2*BesselJ(1, x)+ 2*sum((2*k + 5)*(Psi(k + 3)- Psi(1)- 1)* BesselJ(2*k + 5, x), k = 0..infinity)</code> || <code>2*Sum[(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselJ[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None] == x - 2*BesselJ[1, x]+ 2*Sum[(2*k + 5)*(PolyGamma[k + 3]- PolyGamma[1]- 1)* BesselJ[2*k + 5, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Aborted || Successful [Tested: 3] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E13 10.22.E13] || [[Item:Q3387|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}</math>]] || <code>int(BesselJ(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)</code> || <code>Integrate[BesselJ[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]</code> || Failure || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E13 10.22.E13] || [[Item:Q3387|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{2\nu}@{2z\cos@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}</math>]] || <code>int(BesselJ(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)</code> || <code>Integrate[BesselJ[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]</code> || Failure || Failure || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E14 10.22.E14] || [[Item:Q3388|<math>\int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \pi\cos@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}</math>]] || <code>int(BesselJ(2*nu, 2*z*sin(theta))*cos(2*mu*theta), theta = 0..Pi) = Pi*cos(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)</code> || <code>Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Pi*Cos[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]</code> || Failure || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E14 10.22.E14] || [[Item:Q3388|<math>\int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\cos@{2\mu\theta}\diff{\theta} = \pi\cos@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}</math>]] || <code>int(BesselJ(2*nu, 2*z*sin(theta))*cos(2*mu*theta), theta = 0..Pi) = Pi*cos(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)</code> || <code>Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Pi*Cos[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]</code> || Failure || Failure || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E15 10.22.E15] || [[Item:Q3389|<math>\int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\sin@{2\mu\theta}\diff{\theta} = \pi\sin@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}</math>]] || <code>int(BesselJ(2*nu, 2*z*sin(theta))*sin(2*mu*theta), theta = 0..Pi) = Pi*sin(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)</code> || <code>Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Sin[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Pi*Sin[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]</code> || Failure || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E15 10.22.E15] || [[Item:Q3389|<math>\int_{0}^{\pi}\BesselJ{2\nu}@{2z\sin@@{\theta}}\sin@{2\mu\theta}\diff{\theta} = \pi\sin@{\mu\pi}\BesselJ{\nu+\mu}@{z}\BesselJ{\nu-\mu}@{z}</math>]] || <code>int(BesselJ(2*nu, 2*z*sin(theta))*sin(2*mu*theta), theta = 0..Pi) = Pi*sin(mu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)</code> || <code>Integrate[BesselJ[2*\[Nu], 2*z*Sin[\[Theta]]]*Sin[2*\[Mu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None] == Pi*Sin[\[Mu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]</code> || Failure || Failure || Manual Skip! || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.22.E16 10.22.E16] || [[Item:Q3390|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}^{2}@{z}</math>]] || <code>int(BesselJ(0, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*(BesselJ(n, z))^(2)</code> || <code>Integrate[BesselJ[0, 2*z*Sin[\[Theta]]]*Cos[2*n*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*(BesselJ[n, z])^(2)</code> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
@@ Line 357: / Line 391: @@
 | [https://dlmf.nist.gov/10.22.E18 10.22.E18] || [[Item:Q3392|<math>\int_{0}^{\frac{1}{2}\pi}\BesselY{0}@{2z\sin@@{\theta}}\cos@{2n\theta}\diff{\theta} = \tfrac{1}{2}\pi\BesselJ{n}@{z}\BesselY{n}@{z}</math>]] || <code>int(BesselY(0, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*BesselJ(n, z)*BesselY(n, z)</code> || <code>Integrate[BesselY[0, 2*z*Sin[\[Theta]]]*Cos[2*n*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*BesselJ[n, z]*BesselY[n, z]</code> || Failure || Failure || Successful [Tested: 7] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E19 10.22.E19] || [[Item:Q3393|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = 2^{\nu}\EulerGamma@{\nu+1}z^{-\nu-1}\BesselJ{\mu+\nu+1}@{z}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu + 1)*(cos(theta))^(2*nu + 1), theta = 0..(1)/(2)*Pi) = (2)^(nu)* GAMMA(nu + 1)*(z)^(- nu - 1)* BesselJ(mu + nu + 1, z)</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^(\[Mu]+ 1)*(Cos[\[Theta]])^(2*\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (2)^\[Nu]* Gamma[\[Nu]+ 1]*(z)^(- \[Nu]- 1)* BesselJ[\[Mu]+ \[Nu]+ 1, z]</code> || Successful || Error || - || Successful [Tested: 300]
+| [https://dlmf.nist.gov/10.22.E19 10.22.E19] || [[Item:Q3393|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = 2^{\nu}\EulerGamma@{\nu+1}z^{-\nu-1}\BesselJ{\mu+\nu+1}@{z}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu + 1)*(cos(theta))^(2*nu + 1), theta = 0..(1)/(2)*Pi) = (2)^(nu)* GAMMA(nu + 1)*(z)^(- nu - 1)* BesselJ(mu + nu + 1, z)</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^(\[Mu]+ 1)*(Cos[\[Theta]])^(2*\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (2)^\[Nu]* Gamma[\[Nu]+ 1]*(z)^(- \[Nu]- 1)* BesselJ[\[Mu]+ \[Nu]+ 1, z]</code> || Successful || Aborted || - || Successful [Tested: 300]
+|-
+| [https://dlmf.nist.gov/10.22.E20 10.22.E20] || [[Item:Q3394|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}^{2}@{\tfrac{1}{2}z}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi) = (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*(BesselJ(mu, (1)/(2)*z))^(2)</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^\[Mu]*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*(BesselJ[\[Mu], Divide[1,2]*z])^(2)</code> || Successful || Aborted || - || Successful [Tested: 35]
+|-
+| [https://dlmf.nist.gov/10.22.E21 10.22.E21] || [[Item:Q3395|<math>\int_{0}^{\frac{1}{2}\pi}\BesselY{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}@{\tfrac{1}{2}z}\BesselY{\mu}@{\tfrac{1}{2}z}</math>]] || <code>int(BesselY(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi) = (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*BesselJ(mu, (1)/(2)*z)*BesselY(mu, (1)/(2)*z)</code> || <code>Integrate[BesselY[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^\[Mu]*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*BesselJ[\[Mu], Divide[1,2]*z]*BesselY[\[Mu], Divide[1,2]*z]</code> || Successful || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E20 10.22.E20] || [[Item:Q3394|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}^{2}@{\tfrac{1}{2}z}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi) = (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*(BesselJ(mu, (1)/(2)*z))^(2)</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^\[Mu]*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*(BesselJ[\[Mu], Divide[1,2]*z])^(2)</code> || Successful || Error || - || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.22.E22 10.22.E22] || [[Item:Q3396|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\mu+1}(\cos@@{\theta})^{2\nu+1}\diff{\theta} = \frac{\EulerGamma@{\mu+\tfrac{1}{2}}\EulerGamma@{\nu+\tfrac{1}{2}}\BesselJ{\mu+\nu+\frac{1}{2}}@{z}}{(8\pi z)^{\frac{1}{2}}\EulerGamma@{\mu+\nu+1}}</math>]] || <code>int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*(sin(theta))^(2*mu + 1)*(cos(theta))^(2*nu + 1), theta = 0..(1)/(2)*Pi) = (GAMMA(mu +(1)/(2))*GAMMA(nu +(1)/(2))*BesselJ(mu + nu +(1)/(2), z))/((8*Pi*z)^((1)/(2))* GAMMA(mu + nu + 1))</code> || <code>Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*(Sin[\[Theta]])^(2*\[Mu]+ 1)*(Cos[\[Theta]])^(2*\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[Gamma[\[Mu]+Divide[1,2]]*Gamma[\[Nu]+Divide[1,2]]*BesselJ[\[Mu]+ \[Nu]+Divide[1,2], z],(8*Pi*z)^(Divide[1,2])* Gamma[\[Mu]+ \[Nu]+ 1]]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E21 10.22.E21] || [[Item:Q3395|<math>\int_{0}^{\frac{1}{2}\pi}\BesselY{\mu}@{z\sin@@{\theta}}(\sin@@{\theta})^{\mu}(\cos@@{\theta})^{2\mu}\diff{\theta} = \pi^{\frac{1}{2}}2^{\mu-1}z^{-\mu}\*\EulerGamma@{\mu+\tfrac{1}{2}}\BesselJ{\mu}@{\tfrac{1}{2}z}\BesselY{\mu}@{\tfrac{1}{2}z}</math>]] || <code>int(BesselY(mu, z*sin(theta))*(sin(theta))^(mu)*(cos(theta))^(2*mu), theta = 0..(1)/(2)*Pi) = (Pi)^((1)/(2))* (2)^(mu - 1)* (z)^(- mu)* GAMMA(mu +(1)/(2))*BesselJ(mu, (1)/(2)*z)*BesselY(mu, (1)/(2)*z)</code> || <code>Integrate[BesselY[\[Mu], z*Sin[\[Theta]]]*(Sin[\[Theta]])^\[Mu]*(Cos[\[Theta]])^(2*\[Mu]), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == (Pi)^(Divide[1,2])* (2)^(\[Mu]- 1)* (z)^(- \[Mu])* Gamma[\[Mu]+Divide[1,2]]*BesselJ[\[Mu], Divide[1,2]*z]*BesselY[\[Mu], Divide[1,2]*z]</code> || Successful || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E23 10.22.E23] || [[Item:Q3397|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\alpha-1}\sec@@{\theta}\diff{\theta} = \frac{(\mu+\nu+\alpha)\EulerGamma@{\mu+\alpha}2^{\alpha-1}}{\nu\EulerGamma@{\mu+1}z^{\alpha}}\BesselJ{\mu+\nu+\alpha}@{z}</math>]] || <code>int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*(sin(theta))^(2*alpha - 1)* sec(theta), theta = 0..(1)/(2)*Pi) = ((mu + nu + alpha)* GAMMA(mu + alpha)*(2)^(alpha - 1))/(nu*GAMMA(mu + 1)*(z)^(alpha))*BesselJ(mu + nu + alpha, z)</code> || <code>Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*(Sin[\[Theta]])^(2*\[Alpha]- 1)* Sec[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu]+ \[Alpha])* Gamma[\[Mu]+ \[Alpha]]*(2)^(\[Alpha]- 1),\[Nu]*Gamma[\[Mu]+ 1]*(z)^\[Alpha]]*BesselJ[\[Mu]+ \[Nu]+ \[Alpha], z]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E23 10.22.E23] || [[Item:Q3397|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}(\sin@@{\theta})^{2\alpha-1}\sec@@{\theta}\diff{\theta} = \frac{(\mu+\nu+\alpha)\EulerGamma@{\mu+\alpha}2^{\alpha-1}}{\nu\EulerGamma@{\mu+1}z^{\alpha}}\BesselJ{\mu+\nu+\alpha}@{z}</math>]] || <code>int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*(sin(theta))^(2*alpha - 1)* sec(theta), theta = 0..(1)/(2)*Pi) = ((mu + nu + alpha)* GAMMA(mu + alpha)*(2)^(alpha - 1))/(nu*GAMMA(mu + 1)*(z)^(alpha))*BesselJ(mu + nu + alpha, z)</code> || <code>Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*(Sin[\[Theta]])^(2*\[Alpha]- 1)* Sec[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu]+ \[Alpha])* Gamma[\[Mu]+ \[Alpha]]*(2)^(\[Alpha]- 1),\[Nu]*Gamma[\[Mu]+ 1]*(z)^\[Alpha]]*BesselJ[\[Mu]+ \[Nu]+ \[Alpha], z]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E24 10.22.E24] || [[Item:Q3398|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}\cot@@{\theta}\diff{\theta} = \tfrac{1}{2}\mu^{-1}\BesselJ{\mu+\nu}@{z}</math>]] || <code>int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*cot(theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*(mu)^(- 1)* BesselJ(mu + nu, z)</code> || <code>Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*Cot[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*\[Mu]^(- 1)* BesselJ[\[Mu]+ \[Nu], z]</code> || Failure || Aborted || Skipped - Because timed out || Skip - No test values generated
 |-
-| [https://dlmf.nist.gov/10.22.E24 10.22.E24] || [[Item:Q3398|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin^{2}@@{\theta}}\BesselJ{\nu}@{z\cos^{2}@@{\theta}}\cot@@{\theta}\diff{\theta} = \tfrac{1}{2}\mu^{-1}\BesselJ{\mu+\nu}@{z}</math>]] || <code>int(BesselJ(mu, z*(sin(theta))^(2))*BesselJ(nu, z*(cos(theta))^(2))*cot(theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*(mu)^(- 1)* BesselJ(mu + nu, z)</code> || <code>Integrate[BesselJ[\[Mu], z*(Sin[\[Theta]])^(2)]*BesselJ[\[Nu], z*(Cos[\[Theta]])^(2)]*Cot[\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*\[Mu]^(- 1)* BesselJ[\[Mu]+ \[Nu], z]</code> || Failure || Error || Skipped - Because timed out || Skip - No test values generated
+| [https://dlmf.nist.gov/10.22.E25 10.22.E25] || [[Item:Q3399|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\modBesselI{\nu}@{z\cos@@{\theta}}(\tan@@{\theta})^{\mu+1}\diff{\theta} = \frac{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu}(\tfrac{1}{2}z)^{\mu}}{2\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1}}\BesselJ{\nu}@{z}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*BesselI(nu, z*cos(theta))*(tan(theta))^(mu + 1), theta = 0..(1)/(2)*Pi) = (GAMMA((1)/(2)*nu -(1)/(2)*mu)*((1)/(2)*z)^(mu))/(2*GAMMA((1)/(2)*nu +(1)/(2)*mu + 1))*BesselJ(nu, z)</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*BesselI[\[Nu], z*Cos[\[Theta]]]*(Tan[\[Theta]])^(\[Mu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]]*(Divide[1,2]*z)^\[Mu],2*Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+ 1]]*BesselJ[\[Nu], z]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E25 10.22.E25] || [[Item:Q3399|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\modBesselI{\nu}@{z\cos@@{\theta}}(\tan@@{\theta})^{\mu+1}\diff{\theta} = \frac{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu}(\tfrac{1}{2}z)^{\mu}}{2\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1}}\BesselJ{\nu}@{z}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*BesselI(nu, z*cos(theta))*(tan(theta))^(mu + 1), theta = 0..(1)/(2)*Pi) = (GAMMA((1)/(2)*nu -(1)/(2)*mu)*((1)/(2)*z)^(mu))/(2*GAMMA((1)/(2)*nu +(1)/(2)*mu + 1))*BesselJ(nu, z)</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*BesselI[\[Nu], z*Cos[\[Theta]]]*(Tan[\[Theta]])^(\[Mu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]]*(Divide[1,2]*z)^\[Mu],2*Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+ 1]]*BesselJ[\[Nu], z]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E26 10.22.E26] || [[Item:Q3400|<math>\int_{0}^{\frac{1}{2}\pi}\BesselJ{\mu}@{z\sin@@{\theta}}\BesselJ{\nu}@{\zeta\cos@@{\theta}}(\sin@@{\theta})^{\mu+1}(\cos@@{\theta})^{\nu+1}\diff{\theta} = \frac{z^{\mu}\zeta^{\nu}\BesselJ{\mu+\nu+1}@{\sqrt{\zeta^{2}+z^{2}}}}{(\zeta^{2}+z^{2})^{\frac{1}{2}(\mu+\nu+1)}}</math>]] || <code>int(BesselJ(mu, z*sin(theta))*BesselJ(nu, zeta*cos(theta))*(sin(theta))^(mu + 1)*(cos(theta))^(nu + 1), theta = 0..(1)/(2)*Pi) = ((z)^(mu)* (zeta)^(nu)* BesselJ(mu + nu + 1, sqrt((zeta)^(2)+ (z)^(2))))/(((zeta)^(2)+ (z)^(2))^((1)/(2)*(mu + nu + 1)))</code> || <code>Integrate[BesselJ[\[Mu], z*Sin[\[Theta]]]*BesselJ[\[Nu], \[Zeta]*Cos[\[Theta]]]*(Sin[\[Theta]])^(\[Mu]+ 1)*(Cos[\[Theta]])^(\[Nu]+ 1), {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[(z)^\[Mu]* \[Zeta]^\[Nu]* BesselJ[\[Mu]+ \[Nu]+ 1, Sqrt[\[Zeta]^(2)+ (z)^(2)]],(\[Zeta]^(2)+ (z)^(2))^(Divide[1,2]*(\[Mu]+ \[Nu]+ 1))]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.22.E27 10.22.E27] || [[Item:Q3401|<math>\int_{0}^{x}t\BesselJ{\nu-1}^{2}@{t}\diff{t} = 2\sum_{k=0}^{\infty}(\nu+2k)\BesselJ{\nu+2k}^{2}@{x}</math>]] || <code>int(t*(BesselJ(nu - 1, t))^(2), t = 0..x) = 2*sum((nu + 2*k)* (BesselJ(nu + 2*k, x))^(2), k = 0..infinity)</code> || <code>Integrate[t*(BesselJ[\[Nu]- 1, t])^(2), {t, 0, x}, GenerateConditions->None] == 2*Sum[(\[Nu]+ 2*k)* (BesselJ[\[Nu]+ 2*k, x])^(2), {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Successful || Successful [Tested: 15] || Successful [Tested: 15]
@@ Line 375: / Line 413: @@
 | [https://dlmf.nist.gov/10.22.E29 10.22.E29] || [[Item:Q3403|<math>\int_{0}^{x}t\BesselJ{0}^{2}@{t}\diff{t} = \tfrac{1}{2}x^{2}\left(\BesselJ{0}^{2}@{x}+\BesselJ{1}^{2}@{x}\right)</math>]] || <code>int(t*(BesselJ(0, t))^(2), t = 0..x) = (1)/(2)*(x)^(2)*((BesselJ(0, x))^(2)+ (BesselJ(1, x))^(2))</code> || <code>Integrate[t*(BesselJ[0, t])^(2), {t, 0, x}, GenerateConditions->None] == Divide[1,2]*(x)^(2)*((BesselJ[0, x])^(2)+ (BesselJ[1, x])^(2))</code> || Successful || Successful || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/10.22.E30 10.22.E30] || [[Item:Q3404|<math>\int_{0}^{x}\BesselJ{n}@{t}\BesselJ{n+1}@{t}\diff{t} = \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x}</math>]] || <code>int(BesselJ(n, t)*BesselJ(n + 1, t), t = 0..x) = (1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n)</code> || <code>Integrate[BesselJ[n, t]*BesselJ[n + 1, t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><code>{Plus[-0.6308420033135872, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]], {Rule[n, 3], Rule[x, 1.5]}</code><br><code>Plus[-0.9403627636501156, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[0.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[0.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[0.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[0.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[0.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 0.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2], Times[Power[0.5, -2], Power[Plus[Times[-1, 0.5, BesselJ[0, 0.5]], Times[2, BesselJ[1, 0.5]]], 2]]]]}]][4.0]], {Rule[n, 3], Rule[x, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.22.E30 10.22.E30] || [[Item:Q3404|<math>\int_{0}^{x}\BesselJ{n}@{t}\BesselJ{n+1}@{t}\diff{t} = \tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x}</math>]] || <code>int(BesselJ(n, t)*BesselJ(n + 1, t), t = 0..x) = (1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n)</code> || <code>Integrate[BesselJ[n, t]*BesselJ[n + 1, t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><code>{Plus[-0.6308420033135872, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]], {Rule[n, 3], Rule[x, 1.5]}</code><br><code>Plus[-0.9403627636501156, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[2, ], Power[0.5, 2], []], Times[Plus[-</div></div>
 |-
-| [https://dlmf.nist.gov/10.22.E30 10.22.E30] || [[Item:Q3404|<math>\tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x} = \sum_{k=n+1}^{\infty}\BesselJ{k}^{2}@{x}</math>]] || <code>(1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n) = sum((BesselJ(k, x))^(2), k = n + 1..infinity)</code> || <code>Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None] == Sum[(BesselJ[k, x])^(2), {k, n + 1, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[0.6309837827773054, Times[-1.0, NSum[Power[BesselJ[k, 1.5], 2] <- {k, 4, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]]], {Rule[n, 3], Rule[x, 1.5]}</code><br><code>Plus[0.9403627895513045, Times[-1.0, NSum[Power[BesselJ[k, 0.5], 2] <- {k, 4, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], Power[0.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[0.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[0.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[0.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[0.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 0.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 0.5], 2], Power[BesselJ[1, 0.5], 2], Times[Power[0.5, -2], Power[Plus[Times[-1, 0.5, BesselJ[0, 0.5]], Times[2, BesselJ[1, 0.5]]], 2]]]]}]][4.0]]], {Rule[n, 3], Rule[x, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.22.E30 10.22.E30] || [[Item:Q3404|<math>\tfrac{1}{2}\left(1-\BesselJ{0}^{2}@{x}\right)-\sum_{k=1}^{n}\BesselJ{k}^{2}@{x} = \sum_{k=n+1}^{\infty}\BesselJ{k}^{2}@{x}</math>]] || <code>(1)/(2)*(1 - (BesselJ(0, x))^(2))- sum((BesselJ(k, x))^(2), k = 1..n) = sum((BesselJ(k, x))^(2), k = n + 1..infinity)</code> || <code>Divide[1,2]*(1 - (BesselJ[0, x])^(2))- Sum[(BesselJ[k, x])^(2), {k, 1, n}, GenerateConditions->None] == Sum[(BesselJ[k, x])^(2), {k, n + 1, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[0.6309837827773054, Times[-1.0, NSum[Power[BesselJ[k, 1.5], 2] <- {k, 4, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], Power[1.5, 2], []], Times[Plus[-8, Times[-20, ], Times[-16, Power[, 2]], Times[-4, Power[, 3]], Times[-1, Power[1.5, 2]]], [Plus[1, ]]], Times[Plus[3, Times[2, ]], Plus[8, Times[12, ], Times[4, Power[, 2]], Times[-1, Power[1.5, 2]]], [Plus[2, ]]], Times[Plus[-16, Times[-32, ], Times[-20, Power[, 2]], Times[-4, Power[, 3]], Power[1.5, 2]], [Plus[3, ]]], Times[Plus[1, ], Power[1.5, 2], [Plus[4, ]]]], 0], Equal[[0], 0], Equal[[1], Power[BesselJ[0, 1.5], 2]], Equal[[2], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2]]], Equal[[3], Plus[Power[BesselJ[0, 1.5], 2], Power[BesselJ[1, 1.5], 2], Times[Power[1.5, -2], Power[Plus[Times[-1, 1.5, BesselJ[0, 1.5]], Times[2, BesselJ[1, 1.5]]], 2]]]]}]][4.0]]], {Rule[n, 3], Rule[x, 1.5]}</code><br><code>Plus[</div></div>
 |-
 | [https://dlmf.nist.gov/10.22.E31 10.22.E31] || [[Item:Q3405|<math>\int_{0}^{x}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = 2\sum_{k=0}^{\infty}(-1)^{k}\BesselJ{\mu+\nu+2k+1}@{x}</math>]] || <code>int(BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x) = 2*sum((- 1)^(k)* BesselJ(mu + nu + 2*k + 1, x), k = 0..infinity)</code> || <code>Integrate[BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == 2*Sum[(- 1)^(k)* BesselJ[\[Mu]+ \[Nu]+ 2*k + 1, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Skip - No test values generated
 |-
-| [https://dlmf.nist.gov/10.22.E32 10.22.E32] || [[Item:Q3406|<math>\int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{1-\nu}@{x-t}\diff{t} = \BesselJ{0}@{x}-\cos@@{x}</math>]] || <code>int(BesselJ(nu, t)*BesselJ(1 - nu, x - t), t = 0..x) = BesselJ(0, x)- cos(x)</code> || <code>Integrate[BesselJ[\[Nu], t]*BesselJ[1 - \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == BesselJ[0, x]- Cos[x]</code> || Failure || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E32 10.22.E32] || [[Item:Q3406|<math>\int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{1-\nu}@{x-t}\diff{t} = \BesselJ{0}@{x}-\cos@@{x}</math>]] || <code>int(BesselJ(nu, t)*BesselJ(1 - nu, x - t), t = 0..x) = BesselJ(0, x)- cos(x)</code> || <code>Integrate[BesselJ[\[Nu], t]*BesselJ[1 - \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == BesselJ[0, x]- Cos[x]</code> || Failure || Failure || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E33 10.22.E33] || [[Item:Q3407|<math>\int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{-\nu}@{x-t}\diff{t} = \sin@@{x}</math>]] || <code>int(BesselJ(nu, t)*BesselJ(- nu, x - t), t = 0..x) = sin(x)</code> || <code>Integrate[BesselJ[\[Nu], t]*BesselJ[- \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Sin[x]</code> || Failure || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.22.E33 10.22.E33] || [[Item:Q3407|<math>\int_{0}^{x}\BesselJ{\nu}@{t}\BesselJ{-\nu}@{x-t}\diff{t} = \sin@@{x}</math>]] || <code>int(BesselJ(nu, t)*BesselJ(- nu, x - t), t = 0..x) = sin(x)</code> || <code>Integrate[BesselJ[\[Nu], t]*BesselJ[- \[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Sin[x]</code> || Failure || Failure || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.22.E34 10.22.E34] || [[Item:Q3408|<math>\int_{0}^{x}t^{-1}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = \frac{\BesselJ{\mu+\nu}@{x}}{\mu}</math>]] || <code>int((t)^(- 1)* BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x) = (BesselJ(mu + nu, x))/(mu)</code> || <code>Integrate[(t)^(- 1)* BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Divide[BesselJ[\[Mu]+ \[Nu], x],\[Mu]]</code> || Failure || Failure || - || Skip - No test values generated
+| [https://dlmf.nist.gov/10.22.E34 10.22.E34] || [[Item:Q3408|<math>\int_{0}^{x}t^{-1}\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t} = \frac{\BesselJ{\mu+\nu}@{x}}{\mu}</math>]] || <code>int((t)^(- 1)* BesselJ(mu, t)*BesselJ(nu, x - t), t = 0..x) = (BesselJ(mu + nu, x))/(mu)</code> || <code>Integrate[(t)^(- 1)* BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t], {t, 0, x}, GenerateConditions->None] == Divide[BesselJ[\[Mu]+ \[Nu], x],\[Mu]]</code> || Failure || Failure || Manual Skip! || Skip - No test values generated
 |-
 | [https://dlmf.nist.gov/10.22.E35 10.22.E35] || [[Item:Q3409|<math>\int_{0}^{x}\frac{\BesselJ{\mu}@{t}\BesselJ{\nu}@{x-t}\diff{t}}{t(x-t)} = \frac{(\mu+\nu)\BesselJ{\mu+\nu}@{x}}{\mu\nu x}</math>]] || <code>int((BesselJ(mu, t)*BesselJ(nu, x - t))/(t*(x - t)), t = 0..x) = ((mu + nu)* BesselJ(mu + nu, x))/(mu*nu*x)</code> || <code>Integrate[Divide[BesselJ[\[Mu], t]*BesselJ[\[Nu], x - t],t*(x - t)], {t, 0, x}, GenerateConditions->None] == Divide[(\[Mu]+ \[Nu])* BesselJ[\[Mu]+ \[Nu], x],\[Mu]*\[Nu]*x]</code> || Error || Failure || - || Skip - No test values generated
@@ Line 391: / Line 429: @@
 | [https://dlmf.nist.gov/10.22.E36 10.22.E36] || [[Item:Q3410|<math>\frac{1}{\EulerGamma@{\alpha}}\int_{0}^{x}(x-t)^{\alpha-1}\BesselJ{\nu}@{t}\diff{t} = 2^{\alpha}\sum_{k=0}^{\infty}\frac{(\alpha)_{k}}{k!}\BesselJ{\nu+\alpha+2k}@{x}</math>]] || <code>(1)/(GAMMA(alpha))*int((x - t)^(alpha - 1)* BesselJ(nu, t), t = 0..x) = (2)^(alpha)* sum((alpha[k])/(factorial(k))*BesselJ(nu + alpha + 2*k, x), k = 0..infinity)</code> || <code>Divide[1,Gamma[\[Alpha]]]*Integrate[(x - t)^(\[Alpha]- 1)* BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == (2)^\[Alpha]* Sum[Divide[Subscript[\[Alpha], k],(k)!]*BesselJ[\[Nu]+ \[Alpha]+ 2*k, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Skip - No test values generated
 |-
-| [https://dlmf.nist.gov/10.22.E37 10.22.E37] || [[Item:Q3411|<math>\int_{0}^{1}t\BesselJ{\nu}@{j_{\nu,\ell}t}\BesselJ{\nu}@{j_{\nu,m}t}\diff{t} = \tfrac{1}{2}\left(\BesselJ{\nu}'@{j_{\nu,\ell}}\right)^{2}\Kroneckerdelta{\ell}{m}</math>]] || <code>int(t*BesselJ(nu, j[nu , ell]*t)*BesselJ(nu, j[nu , m]*t), t = 0..1) = (1)/(2)*(diff( BesselJ(nu, j[nu , ell]), j[nu , ell]$(1) ))^(2)* KroneckerDelta[ell, m]</code> || <code>Integrate[t*BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[j, \[Nu], m]*t], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(D[BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]], {Subscript[j, \[Nu], \[ScriptL]], 1}])^(2)* KroneckerDelta[\[ScriptL], m]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[m, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[m, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.22.E37 10.22.E37] || [[Item:Q3411|<math>\int_{0}^{1}t\BesselJ{\nu}@{j_{\nu,\ell}t}\BesselJ{\nu}@{j_{\nu,m}t}\diff{t} = \tfrac{1}{2}\left(\BesselJ{\nu}'@{j_{\nu,\ell}}\right)^{2}\Kroneckerdelta{\ell}{m}</math>]] || <code>int(t*BesselJ(nu, j[nu , ell]*t)*BesselJ(nu, j[nu , m]*t), t = 0..1) = (1)/(2)*(diff( BesselJ(nu, j[nu , ell]), j[nu , ell]$(1) ))^(2)* KroneckerDelta[ell, m]</code> || <code>Integrate[t*BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[j, \[Nu], m]*t], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(D[BesselJ[\[Nu], Subscript[j, \[Nu], \[ScriptL]]], {Subscript[j, \[Nu], \[ScriptL]], 1}])^(2)* KroneckerDelta[\[ScriptL], m]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[m, 1], Rule[ℓ, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[m, 1], Rule[ℓ, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, ν, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
 | [https://dlmf.nist.gov/10.22.E38 10.22.E38] || [[Item:Q3412|<math>\int_{0}^{1}t\BesselJ{\nu}@{\alpha_{\ell}t}\BesselJ{\nu}@{\alpha_{m}t}\diff{t} = \left(\frac{a^{2}}{b^{2}}+\alpha_{\ell}^{2}-\nu^{2}\right)\frac{(\BesselJ{\nu}@{\alpha_{\ell}})^{2}}{2\alpha_{\ell}^{2}}\Kroneckerdelta{\ell}{m}</math>]] || <code>int(t*BesselJ(nu, alpha[ell]*t)*BesselJ(nu, alpha[m]*t), t = 0..1) ((BesselJ(nu, alpha[ell]))^(2))/(2*alpha(alpha[ell])^(2))*KroneckerDelta[ell, m]</code> || <code>Integrate[t*BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]*t]*BesselJ[\[Nu], Subscript[\[Alpha], m]*t], {t, 0, 1}, GenerateConditions->None] Divide[(BesselJ[\[Nu], Subscript[\[Alpha], \[ScriptL]]])^(2),2*\[Alpha](Subscript[\[Alpha], \[ScriptL]])^(2)]*KroneckerDelta[\[ScriptL], m]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[m, 1], Rule[α, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[m, 2], Rule[α, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[α, ℓ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
@@ Line 398: / Line 436: @@
 |-
 | [https://dlmf.nist.gov/10.22.E39 10.22.E39] || [[Item:Q3413|<math>\int_{0}^{x}\frac{1-\BesselJ{0}@{t}}{t}\diff{t} = \sum_{k=1}^{\infty}(-1)^{k-1}\frac{(\frac{1}{2}x)^{2k}}{2k(k!)^{2}}</math>]] || <code>int((1 - BesselJ(0, t))/(t), t = 0..x) = sum((- 1)^(k - 1)*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity)</code> || <code>Integrate[Divide[1 - BesselJ[0, t],t], {t, 0, x}, GenerateConditions->None] == Sum[(- 1)^(k - 1)*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 3]
+|-
+| [https://dlmf.nist.gov/10.22.E40 10.22.E40] || [[Item:Q3414|<math>\int_{x}^{\infty}\frac{\BesselY{0}@{t}}{t}\diff{t} = -\frac{1}{\pi}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi}{6}+\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\*\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}</math>]] || <code>int((BesselY(0, t))/(t), t = x..infinity) = -(1)/(Pi)*(ln((1)/(2)*x)+ gamma)^(2)+(Pi)/(6)+(2)/(Pi)*sum((- 1)^(k)*(Psi(k + 1)+(1)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity)</code> || <code>Integrate[Divide[BesselY[0, t],t], {t, x, Infinity}, GenerateConditions->None] == -Divide[1,Pi]*(Log[Divide[1,2]*x]+ EulerGamma)^(2)+Divide[Pi,6]+Divide[2,Pi]*Sum[(- 1)^(k)*(PolyGamma[k + 1]+Divide[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]</code> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.22.E41 10.22.E41] || [[Item:Q3415|<math>\int_{0}^{\infty}\BesselJ{\nu}@{t}\diff{t} = 1</math>]] || <code>int(BesselJ(nu, t), t = 0..infinity) = 1</code> || <code>Integrate[BesselJ[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == 1</code> || Successful || Successful || - || Successful [Tested: 8]
 |-
-| [https://dlmf.nist.gov/10.22.E42 10.22.E42] || [[Item:Q3416|<math>\int_{0}^{\infty}\BesselY{\nu}@{t}\diff{t} = -\tan@{\tfrac{1}{2}\nu\pi}</math>]] || <code>int(BesselY(nu, t), t = 0..infinity) = - tan((1)/(2)*nu*Pi)</code> || <code>Integrate[BesselY[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == - Tan[Divide[1,2]*\[Nu]*Pi]</code> || Successful || Error || - || Successful [Tested: 6]
+| [https://dlmf.nist.gov/10.22.E42 10.22.E42] || [[Item:Q3416|<math>\int_{0}^{\infty}\BesselY{\nu}@{t}\diff{t} = -\tan@{\tfrac{1}{2}\nu\pi}</math>]] || <code>int(BesselY(nu, t), t = 0..infinity) = - tan((1)/(2)*nu*Pi)</code> || <code>Integrate[BesselY[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == - Tan[Divide[1,2]*\[Nu]*Pi]</code> || Successful || Aborted || - || Successful [Tested: 6]
 |-
 | [https://dlmf.nist.gov/10.22.E43 10.22.E43] || [[Item:Q3417|<math>\int_{0}^{\infty}t^{\mu}\BesselJ{\nu}@{t}\diff{t} = 2^{\mu}\frac{\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+\tfrac{1}{2}}}</math>]] || <code>int((t)^(mu)* BesselJ(nu, t), t = 0..infinity) = (2)^(mu)*(GAMMA((1)/(2)*nu +(1)/(2)*mu +(1)/(2)))/(GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)))</code> || <code>Integrate[(t)^\[Mu]* BesselJ[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == (2)^\[Mu]*Divide[Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]+Divide[1,2]],Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]]</code> || Successful || Successful || - || Successful [Tested: 10]
 |-
-| [https://dlmf.nist.gov/10.22.E55 10.22.E55] || [[Item:Q3429|<math>\int_{0}^{\infty}t^{-1}\BesselJ{\nu+2\ell+1}@{t}\BesselJ{\nu+2m+1}@{t}\diff{t} = \frac{\Kroneckerdelta{\ell}{m}}{2(2\ell+\nu+1)}</math>]] || <code>int((t)^(- 1)* BesselJ(nu + 2*ell + 1, t)*BesselJ(nu + 2*m + 1, t), t = 0..infinity) = (KroneckerDelta[ell, m])/(2*(2*ell + nu + 1))</code> || <code>Integrate[(t)^(- 1)* BesselJ[\[Nu]+ 2*\[ScriptL]+ 1, t]*BesselJ[\[Nu]+ 2*m + 1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[KroneckerDelta[\[ScriptL], m],2*(2*\[ScriptL]+ \[Nu]+ 1)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Plus[Times[-0.5, Power[Plus[Complex[1.8660254037844388, 0.49999999999999994], Times[2.0, ℓ]], -1], KroneckerDelta[1.0, ℓ]], Times[0.15915494309189535, Power[Plus[1.0, Times[-1.0, ℓ]], -1], Power[Plus[Complex[2.866025403784439, 0.49999999999999994], ℓ], -1], Sin[Times[3.141592653589793, Plus[1.0, Times[-1.0, ℓ]]]]]] <- {Rule[m, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Times[-0.5, Power[Plus[Complex[1.8660254037844388, 0.49999999999999994], Times[2.0, ℓ]], -1], KroneckerDelta[2.0, ℓ]], Times[0.15915494309189535, Power[Plus[2.0, Times[-1.0, ℓ]], -1], Power[Plus[Complex[3.866025403784439, 0.49999999999999994], ℓ], -1], Sin[Times[3.141592653589793, Plus[2.0, Times[-1.0, ℓ]]]]]] <- {Rule[m, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.22.E44 10.22.E44] || [[Item:Q3418|<math>\int_{0}^{\infty}t^{\mu}\BesselY{\nu}@{t}\diff{t} = \frac{2^{\mu}}{\pi}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}}\sin@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\pi</math>]] || <code>int((t)^(mu)* BesselY(nu, t), t = 0..infinity) = ((2)^(mu))/(Pi)*GAMMA((1)/(2)*mu +(1)/(2)*nu +(1)/(2))*GAMMA((1)/(2)*mu -(1)/(2)*nu +(1)/(2))*sin((1)/(2)*mu -(1)/(2)*nu)*Pi</code> || <code>Integrate[(t)^\[Mu]* BesselY[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[(2)^\[Mu],Pi]*Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]+Divide[1,2]]*Sin[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Pi</code> || Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><code>{Complex[-0.5512405929316078, 0.2551977660147906] <- {Rule[μ, 0], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.26217720344291356, -0.18052742798771904] <- {Rule[μ, 0], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E45 10.22.E45] || [[Item:Q3419|<math>\int_{0}^{\infty}\frac{1-\BesselJ{0}@{t}}{t^{\mu}}\diff{t} = -\frac{\pi\sec@{\frac{1}{2}\mu\pi}}{2^{\mu}\EulerGamma^{2}@{\frac{1}{2}\mu+\frac{1}{2}}}</math>]] || <code>int((1 - BesselJ(0, t))/((t)^(mu)), t = 0..infinity) = -(Pi*sec((1)/(2)*mu*Pi))/((2)^(mu)* (GAMMA((1)/(2)*mu +(1)/(2)))^(2))</code> || <code>Integrate[Divide[1 - BesselJ[0, t],(t)^\[Mu]], {t, 0, Infinity}, GenerateConditions->None] == -Divide[Pi*Sec[Divide[1,2]*\[Mu]*Pi],(2)^\[Mu]* (Gamma[Divide[1,2]*\[Mu]+Divide[1,2]])^(2)]</code> || Error || Aborted || - || Successful [Tested: 10]
+|-
+| [https://dlmf.nist.gov/10.22.E46 10.22.E46] || [[Item:Q3420|<math>\int_{0}^{\infty}\frac{t^{\nu+1}\BesselJ{\nu}@{at}}{(t^{2}+b^{2})^{\mu+1}}\diff{t} = \frac{a^{\mu}b^{\nu-\mu}}{2^{\mu}\EulerGamma@{\mu+1}}\modBesselK{\nu-\mu}@{ab}</math>]] || <code>int(((t)^(nu + 1)* BesselJ(nu, a*t))/(((t)^(2)+ (b)^(2))^(mu + 1)), t = 0..infinity) = ((a)^(mu)* (b)^(nu - mu))/((2)^(mu)* GAMMA(mu + 1))*BesselK(nu - mu, a*b)</code> || <code>Integrate[Divide[(t)^(\[Nu]+ 1)* BesselJ[\[Nu], a*t],((t)^(2)+ (b)^(2))^(\[Mu]+ 1)], {t, 0, Infinity}, GenerateConditions->None] == Divide[(a)^\[Mu]* (b)^(\[Nu]- \[Mu]),(2)^\[Mu]* Gamma[\[Mu]+ 1]]*BesselK[\[Nu]- \[Mu], a*b]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E47 10.22.E47] || [[Item:Q3421|<math>\int_{0}^{\infty}\frac{t^{\nu}\BesselY{\nu}@{at}}{t^{2}+b^{2}}\diff{t} = -b^{\nu-1}\modBesselK{\nu}@{ab}</math>]] || <code>int(((t)^(nu)* BesselY(nu, a*t))/((t)^(2)+ (b)^(2)), t = 0..infinity) = - (b)^(nu - 1)* BesselK(nu, a*b)</code> || <code>Integrate[Divide[(t)^\[Nu]* BesselY[\[Nu], a*t],(t)^(2)+ (b)^(2)], {t, 0, Infinity}, GenerateConditions->None] == - (b)^(\[Nu]- 1)* BesselK[\[Nu], a*b]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E48 10.22.E48] || [[Item:Q3422|<math>\int_{0}^{\infty}\BesselJ{\mu}@{x\cosh@@{\phi}}(\cosh@@{\phi})^{1-\mu}(\sinh@@{\phi})^{2\nu+1}\diff{\phi} = 2^{\nu}\EulerGamma@{\nu+1}x^{-\nu-1}\BesselJ{\mu-\nu-1}@{x}</math>]] || <code>int(BesselJ(mu, x*cosh(phi))*(cosh(phi))^(1 - mu)*(sinh(phi))^(2*nu + 1), phi = 0..infinity) = (2)^(nu)* GAMMA(nu + 1)*(x)^(- nu - 1)* BesselJ(mu - nu - 1, x)</code> || <code>Integrate[BesselJ[\[Mu], x*Cosh[\[Phi]]]*(Cosh[\[Phi]])^(1 - \[Mu])*(Sinh[\[Phi]])^(2*\[Nu]+ 1), {\[Phi], 0, Infinity}, GenerateConditions->None] == (2)^\[Nu]* Gamma[\[Nu]+ 1]*(x)^(- \[Nu]- 1)* BesselJ[\[Mu]- \[Nu]- 1, x]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E49 10.22.E49] || [[Item:Q3423|<math>\int_{0}^{\infty}t^{\mu-1}e^{-at}\BesselJ{\nu}@{bt}\diff{t} = \frac{(\tfrac{1}{2}b)^{\nu}}{a^{\mu+\nu}}\EulerGamma@{\mu+\nu}\*\hyperOlverF@{\frac{\mu+\nu}{2}}{\frac{\mu+\nu+1}{2}}{\nu+1}{-\frac{b^{2}}{a^{2}}}</math>]] || <code>int((t)^(mu - 1)* exp(- a*t)*BesselJ(nu, b*t), t = 0..infinity) = (((1)/(2)*b)^(nu))/((a)^(mu + nu))*GAMMA(mu + nu)* hypergeom([(mu + nu)/(2), (mu + nu + 1)/(2)], [nu + 1], -((b)^(2))/((a)^(2)))/GAMMA(nu + 1)</code> || <code>Integrate[(t)^(\[Mu]- 1)* Exp[- a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Divide[1,2]*b)^\[Nu],(a)^(\[Mu]+ \[Nu])]*Gamma[\[Mu]+ \[Nu]]* Hypergeometric2F1Regularized[Divide[\[Mu]+ \[Nu],2], Divide[\[Mu]+ \[Nu]+ 1,2], \[Nu]+ 1, -Divide[(b)^(2),(a)^(2)]]</code> || Error || Aborted || - || Successful [Tested: 0]
+|-
+| [https://dlmf.nist.gov/10.22.E50 10.22.E50] || [[Item:Q3424|<math>\int_{0}^{\infty}t^{\mu-1}e^{-at}\BesselY{\nu}@{bt}\diff{t} = \cot@{\nu\pi}\frac{(\tfrac{1}{2}b)^{\nu}\EulerGamma@{\mu+\nu}}{(a^{2}+b^{2})^{\frac{1}{2}(\mu+\nu)}}\*\hyperOlverF@{\frac{\mu+\nu}{2}}{\frac{1-\mu+\nu}{2}}{\nu+1}{\frac{b^{2}}{a^{2}+b^{2}}}-\csc@{\nu\pi}\frac{(\tfrac{1}{2}b)^{-\nu}\EulerGamma@{\mu-\nu}}{(a^{2}+b^{2})^{\frac{1}{2}(\mu-\nu)}}\*\hyperOlverF@{\frac{\mu-\nu}{2}}{\frac{1-\mu-\nu}{2}}{1-\nu}{\frac{b^{2}}{a^{2}+b^{2}}}</math>]] || <code>int((t)^(mu - 1)* exp(- a*t)*BesselY(nu, b*t), t = 0..infinity) = cot(nu*Pi)*(((1)/(2)*b)^(nu)* GAMMA(mu + nu))/(((a)^(2)+ (b)^(2))^((1)/(2)*(mu + nu)))* hypergeom([(mu + nu)/(2), (1 - mu + nu)/(2)], [nu + 1], ((b)^(2))/((a)^(2)+ (b)^(2)))/GAMMA(nu + 1)- csc(nu*Pi)*(((1)/(2)*b)^(- nu)* GAMMA(mu - nu))/(((a)^(2)+ (b)^(2))^((1)/(2)*(mu - nu)))* hypergeom([(mu - nu)/(2), (1 - mu - nu)/(2)], [1 - nu], ((b)^(2))/((a)^(2)+ (b)^(2)))/GAMMA(1 - nu)</code> || <code>Integrate[(t)^(\[Mu]- 1)* Exp[- a*t]*BesselY[\[Nu], b*t], {t, 0, Infinity}, GenerateConditions->None] == Cot[\[Nu]*Pi]*Divide[(Divide[1,2]*b)^\[Nu]* Gamma[\[Mu]+ \[Nu]],((a)^(2)+ (b)^(2))^(Divide[1,2]*(\[Mu]+ \[Nu]))]* Hypergeometric2F1Regularized[Divide[\[Mu]+ \[Nu],2], Divide[1 - \[Mu]+ \[Nu],2], \[Nu]+ 1, Divide[(b)^(2),(a)^(2)+ (b)^(2)]]- Csc[\[Nu]*Pi]*Divide[(Divide[1,2]*b)^(- \[Nu])* Gamma[\[Mu]- \[Nu]],((a)^(2)+ (b)^(2))^(Divide[1,2]*(\[Mu]- \[Nu]))]* Hypergeometric2F1Regularized[Divide[\[Mu]- \[Nu],2], Divide[1 - \[Mu]- \[Nu],2], 1 - \[Nu], Divide[(b)^(2),(a)^(2)+ (b)^(2)]]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E51 10.22.E51] || [[Item:Q3425|<math>\int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}t^{\nu+1}\diff{t} = \frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp@{-\frac{b^{2}}{4p^{2}}}</math>]] || <code>int(BesselJ(nu, b*t)*exp(- (p)^(2)* (t)^(2))*(t)^(nu + 1), t = 0..infinity) = ((b)^(nu))/((2*(p)^(2))^(nu + 1))*exp(-((b)^(2))/(4*(p)^(2)))</code> || <code>Integrate[BesselJ[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)]*(t)^(\[Nu]+ 1), {t, 0, Infinity}, GenerateConditions->None] == Divide[(b)^\[Nu],(2*(p)^(2))^(\[Nu]+ 1)]*Exp[-Divide[(b)^(2),4*(p)^(2)]]</code> || Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [151 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.06577510728447342, -0.5886826409090221] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.0556301041786353, -0.2359104145157832] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E52 10.22.E52] || [[Item:Q3426|<math>\int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{-\frac{b^{2}}{8p^{2}}}\modBesselI{\ifrac{\nu}{2}}@{\frac{b^{2}}{8p^{2}}}</math>]] || <code>int(BesselJ(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(2*p)*exp(-((b)^(2))/(8*(p)^(2)))*BesselI((nu)/(2), ((b)^(2))/(8*(p)^(2)))</code> || <code>Integrate[BesselJ[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],2*p]*Exp[-Divide[(b)^(2),8*(p)^(2)]]*BesselI[Divide[\[Nu],2], Divide[(b)^(2),8*(p)^(2)]]</code> || Error || Aborted || - || Skip - No test values generated
 |-
-| [https://dlmf.nist.gov/10.23.E3 10.23.E3] || [[Item:Q3455|<math>\BesselJ{0}^{2}@{z}+2\sum_{k=1}^{\infty}\BesselJ{k}^{2}@{z} = 1</math>]] || <code>(BesselJ(0, z))^(2)+ 2*sum((BesselJ(k, z))^(2), k = 1..infinity) = 1</code> || <code>(BesselJ[0, z])^(2)+ 2*Sum[(BesselJ[k, z])^(2), {k, 1, Infinity}, GenerateConditions->None] == 1</code> || Error || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.22.E53 10.22.E53] || [[Item:Q3427|<math>\int_{0}^{\infty}\BesselY{2\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = -\frac{\sqrt{\pi}}{2p}\exp@{-\frac{b^{2}}{8p^{2}}}\left(\modBesselI{\nu}@{\frac{b^{2}}{8p^{2}}}\tan@{\nu\pi}+\frac{1}{\pi}\modBesselK{\nu}@{\frac{b^{2}}{8p^{2}}}\sec@{\nu\pi}\right)</math>]] || <code>int(BesselY(2*nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = -(sqrt(Pi))/(2*p)*exp(-((b)^(2))/(8*(p)^(2)))*(BesselI(nu, ((b)^(2))/(8*(p)^(2)))*tan(nu*Pi)+(1)/(Pi)*BesselK(nu, ((b)^(2))/(8*(p)^(2)))*sec(nu*Pi))</code> || <code>Integrate[BesselY[2*\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == -Divide[Sqrt[Pi],2*p]*Exp[-Divide[(b)^(2),8*(p)^(2)]]*(BesselI[\[Nu], Divide[(b)^(2),8*(p)^(2)]]*Tan[\[Nu]*Pi]+Divide[1,Pi]*BesselK[\[Nu], Divide[(b)^(2),8*(p)^(2)]]*Sec[\[Nu]*Pi])</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E54 10.22.E54] || [[Item:Q3428|<math>\int_{0}^{\infty}\BesselJ{\nu}@{bt}\exp@{-p^{2}t^{2}}t^{\mu-1}\diff{t} = \frac{(\tfrac{1}{2}b/p)^{\nu}\EulerGamma@{\tfrac{1}{2}\nu+\tfrac{1}{2}\mu}}{2p^{\mu}}\exp@{-\frac{b^{2}}{4p^{2}}}\*\OlverconfhyperM@{\tfrac{1}{2}\nu-\tfrac{1}{2}\mu+1}{\nu+1}{\frac{b^{2}}{4p^{2}}}</math>]] || <code>int(BesselJ(nu, b*t)*exp(- (p)^(2)* (t)^(2))*(t)^(mu - 1), t = 0..infinity) = (((1)/(2)*b/ p)^(nu)* GAMMA((1)/(2)*nu +(1)/(2)*mu))/(2*(p)^(mu))*exp(-((b)^(2))/(4*(p)^(2)))* KummerM((1)/(2)*nu -(1)/(2)*mu + 1, nu + 1, ((b)^(2))/(4*(p)^(2)))/GAMMA(nu + 1)</code> || <code>Integrate[BesselJ[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)]*(t)^(\[Mu]- 1), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Divide[1,2]*b/ p)^\[Nu]* Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]],2*(p)^\[Mu]]*Exp[-Divide[(b)^(2),4*(p)^(2)]]* Hypergeometric1F1Regularized[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+ 1, \[Nu]+ 1, Divide[(b)^(2),4*(p)^(2)]]</code> || Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{Complex[0.07541885663346475, -0.6281916024632631] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1002850405400357, -0.7734416454563844] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E55 10.22.E55] || [[Item:Q3429|<math>\int_{0}^{\infty}t^{-1}\BesselJ{\nu+2\ell+1}@{t}\BesselJ{\nu+2m+1}@{t}\diff{t} = \frac{\Kroneckerdelta{\ell}{m}}{2(2\ell+\nu+1)}</math>]] || <code>int((t)^(- 1)* BesselJ(nu + 2*ell + 1, t)*BesselJ(nu + 2*m + 1, t), t = 0..infinity) = (KroneckerDelta[ell, m])/(2*(2*ell + nu + 1))</code> || <code>Integrate[(t)^(- 1)* BesselJ[\[Nu]+ 2*\[ScriptL]+ 1, t]*BesselJ[\[Nu]+ 2*m + 1, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[KroneckerDelta[\[ScriptL], m],2*(2*\[ScriptL]+ \[Nu]+ 1)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 54]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[m, 1], Rule[ℓ, 1], Rule[ν, Rational[-3, 2]]}</code><br><code>Indeterminate <- {Rule[m, 2], Rule[ℓ, 2], Rule[ν, Rational[-3, 2]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E56 10.22.E56] || [[Item:Q3430|<math>\int_{0}^{\infty}\frac{\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{a^{\mu}\EulerGamma@{\frac{1}{2}\nu+\frac{1}{2}\mu-\frac{1}{2}\lambda+\frac{1}{2}}}{2^{\lambda}b^{\mu-\lambda+1}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\lambda+\frac{1}{2}}}\*\hyperOlverF@{\tfrac{1}{2}(\mu+\nu-\lambda+1)}{\tfrac{1}{2}(\mu-\nu-\lambda+1)}{\mu+1}{\frac{a^{2}}{b^{2}}}</math>]] || <code>int((BesselJ(mu, a*t)*BesselJ(nu, b*t))/((t)^(lambda)), t = 0..infinity) = ((a)^(mu)* GAMMA((1)/(2)*nu +(1)/(2)*mu -(1)/(2)*lambda +(1)/(2)))/((2)^(lambda)* (b)^(mu - lambda + 1)* GAMMA((1)/(2)*nu -(1)/(2)*mu +(1)/(2)*lambda +(1)/(2)))* hypergeom([(1)/(2)*(mu + nu - lambda + 1), (1)/(2)*(mu - nu - lambda + 1)], [mu + 1], ((a)^(2))/((b)^(2)))/GAMMA(mu + 1)</code> || <code>Integrate[Divide[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], b*t],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(a)^\[Mu]* Gamma[Divide[1,2]*\[Nu]+Divide[1,2]*\[Mu]-Divide[1,2]*\[Lambda]+Divide[1,2]],(2)^\[Lambda]* (b)^(\[Mu]- \[Lambda]+ 1)* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]*\[Lambda]+Divide[1,2]]]* Hypergeometric2F1Regularized[Divide[1,2]*(\[Mu]+ \[Nu]- \[Lambda]+ 1), Divide[1,2]*(\[Mu]- \[Nu]- \[Lambda]+ 1), \[Mu]+ 1, Divide[(a)^(2),(b)^(2)]]</code> || Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.12507202091813296, -0.11002587193353452] <- {Rule[a, 1.5], Rule[b, 2], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.017959797138118128, 0.3252875517547388] <- {Rule[a, 1.5], Rule[b, 2], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E57 10.22.E57] || [[Item:Q3431|<math>\int_{0}^{\infty}\frac{\BesselJ{\mu}@{at}\BesselJ{\nu}@{at}}{t^{\lambda}}\diff{t} = \frac{(\frac{1}{2}a)^{\lambda-1}\EulerGamma@{\frac{1}{2}\mu+\frac{1}{2}\nu-\frac{1}{2}\lambda+\frac{1}{2}}\EulerGamma@{\lambda}}{2\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\mu-\frac{1}{2}\nu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}\nu+\frac{1}{2}}}</math>]] || <code>int((BesselJ(mu, a*t)*BesselJ(nu, a*t))/((t)^(lambda)), t = 0..infinity) = (((1)/(2)*a)^(lambda - 1)* GAMMA((1)/(2)*mu +(1)/(2)*nu -(1)/(2)*lambda +(1)/(2))*GAMMA(lambda))/(2*GAMMA((1)/(2)*lambda +(1)/(2)*nu -(1)/(2)*mu +(1)/(2))*GAMMA((1)/(2)*lambda +(1)/(2)*mu -(1)/(2)*nu +(1)/(2))*GAMMA((1)/(2)*lambda +(1)/(2)*mu +(1)/(2)*nu +(1)/(2)))</code> || <code>Integrate[Divide[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], a*t],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(Divide[1,2]*a)^(\[Lambda]- 1)* Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2]]*Gamma[\[Lambda]],2*Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]*\[Nu]-Divide[1,2]*\[Mu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]+Divide[1,2]]]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E58 10.22.E58] || [[Item:Q3432|<math>\int_{0}^{\infty}\frac{\BesselJ{\nu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{(ab)^{\nu}\EulerGamma@{\nu-\frac{1}{2}\lambda+\frac{1}{2}}}{2^{\lambda}(a^{2}+b^{2})^{\nu-\frac{1}{2}\lambda+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\lambda+\frac{1}{2}}}\hyperOlverF@{\frac{2\nu+1-\lambda}{4}}{\frac{2\nu+3-\lambda}{4}}{\nu+1}{\frac{4a^{2}b^{2}}{(a^{2}+b^{2})^{2}}}</math>]] || <code>int((BesselJ(nu, a*t)*BesselJ(nu, b*t))/((t)^(lambda)), t = 0..infinity) = ((a*b)^(nu)* GAMMA(nu -(1)/(2)*lambda +(1)/(2)))/((2)^(lambda)*((a)^(2)+ (b)^(2))^(nu -(1)/(2)*lambda +(1)/(2))* GAMMA((1)/(2)*lambda +(1)/(2)))*hypergeom([(2*nu + 1 - lambda)/(4), (2*nu + 3 - lambda)/(4)], [nu + 1], (4*(a)^(2)* (b)^(2))/(((a)^(2)+ (b)^(2))^(2)))/GAMMA(nu + 1)</code> || <code>Integrate[Divide[BesselJ[\[Nu], a*t]*BesselJ[\[Nu], b*t],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(a*b)^\[Nu]* Gamma[\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2]],(2)^\[Lambda]*((a)^(2)+ (b)^(2))^(\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2])* Gamma[Divide[1,2]*\[Lambda]+Divide[1,2]]]*Hypergeometric2F1Regularized[Divide[2*\[Nu]+ 1 - \[Lambda],4], Divide[2*\[Nu]+ 3 - \[Lambda],4], \[Nu]+ 1, Divide[4*(a)^(2)* (b)^(2),((a)^(2)+ (b)^(2))^(2)]]</code> || Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [209 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.13393539357334844, 0.1322614378889556] <- {Rule[a, -1.5], Rule[b, -0.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.07230690300251369, -0.15068591568973605] <- {Rule[a, -1.5], Rule[b, -0.5], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.22.E66 10.22.E66] || [[Item:Q3440|<math>\int_{0}^{\infty}e^{-at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}\diff{t} = \frac{1}{\pi(bc)^{\frac{1}{2}}}\*\assLegendreQ[]{\nu-\frac{1}{2}}@{\frac{a^{2}+b^{2}+c^{2}}{2bc}}</math>]] || <code>int(exp(- a*t)*BesselJ(nu, b*t)*BesselJ(nu, c*t), t = 0..infinity) = (1)/(Pi*(b*c)^((1)/(2)))* LegendreQ(nu -(1)/(2), ((a)^(2)+ (b)^(2)+ (c)^(2))/(2*b*c))</code> || <code>Integrate[Exp[- a*t]*BesselJ[\[Nu], b*t]*BesselJ[\[Nu], c*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,Pi*(b*c)^(Divide[1,2])]* LegendreQ[\[Nu]-Divide[1,2], 0, 3, Divide[(a)^(2)+ (b)^(2)+ (c)^(2),2*b*c]]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E67 10.22.E67] || [[Item:Q3441|<math>\int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\BesselJ{\nu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \frac{1}{2p^{2}}\exp@{-\frac{a^{2}+b^{2}}{4p^{2}}}\modBesselI{\nu}\left(\frac{ab}{2p^{2}}\right)</math>]] || <code>int(t*exp(- (p)^(2)* (t)^(2))*BesselJ(nu, a*t)*BesselJ(nu, b*t), t = 0..infinity) = (1)/(2*(p)^(2))*exp(-((a)^(2)+ (b)^(2))/(4*(p)^(2)))*BesselI(nu, (a*b)/(2*(p)^(2)))</code> || <code>Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselJ[\[Nu], a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2*(p)^(2)]*Exp[-Divide[(a)^(2)+ (b)^(2),4*(p)^(2)]]*BesselI[\[Nu], Divide[a*b,2*(p)^(2)]]</code> || Translation Error || Translation Error || - || -
+|-
+| [https://dlmf.nist.gov/10.22.E68 10.22.E68] || [[Item:Q3442|<math>\int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\BesselJ{0}@{at}\BesselY{0}@{at}\diff{t} = -\frac{1}{2\pi p^{2}}\exp@{-\frac{a^{2}}{2p^{2}}}\modBesselK{0}\left(\frac{a^{2}}{2p^{2}}\right)</math>]] || <code>int(t*exp(- (p)^(2)* (t)^(2))*BesselJ(0, a*t)*BesselY(0, a*t), t = 0..infinity) = -(1)/(2*Pi*(p)^(2))*exp(-((a)^(2))/(2*(p)^(2)))*BesselK(0, ((a)^(2))/(2*(p)^(2)))</code> || <code>Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselJ[0, a*t]*BesselY[0, a*t], {t, 0, Infinity}, GenerateConditions->None] == -Divide[1,2*Pi*(p)^(2)]*Exp[-Divide[(a)^(2),2*(p)^(2)]]*BesselK[0, Divide[(a)^(2),2*(p)^(2)]]</code> || Translation Error || Translation Error || - || -
+|-
+| [https://dlmf.nist.gov/10.22.E70 10.22.E70] || [[Item:Q3444|<math>\int_{0}^{\infty}\BesselY{\nu}@{at}\BesselJ{\nu+1}@{bt}\frac{t\diff{t}}{t^{2}-z^{2}} = \frac{1}{2}\pi\BesselJ{\nu+1}@{bz}\HankelH{1}{\nu}@{az}</math>]] || <code>int(BesselY(nu, a*t)*BesselJ(nu + 1, b*t)*(t)/((t)^(2)- (z)^(2)), t = 0..infinity) = (1)/(2)*Pi*BesselJ(nu + 1, b*z)*HankelH1(nu, a*z)</code> || <code>Integrate[BesselY[\[Nu], a*t]*BesselJ[\[Nu]+ 1, b*t]*Divide[t,(t)^(2)- (z)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*BesselJ[\[Nu]+ 1, b*z]*HankelH1[\[Nu], a*z]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.22.E71 10.22.E71] || [[Item:Q3445|<math>\int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1-\mu}\diff{t} = \frac{(bc)^{\mu-1}(\sin@@{\phi})^{\mu-\frac{1}{2}}}{(2\pi)^{\frac{1}{2}}a^{\mu}}\FerrersP[\frac{1}{2}-\mu]{\nu-\frac{1}{2}}(\cos@@{\phi})</math>]] || <code>int(BesselJ(mu, a*t)*BesselJ(nu, b*t)*BesselJ(nu, c*t)*(t)^(1 - mu), t = 0..infinity) = ((b*c)^(mu - 1)*(sin(phi))^(mu -(1)/(2)))/((2*Pi)^((1)/(2))* (a)^(mu))*LegendreP(nu -(1)/(2), (1)/(2)- mu, cos(phi))</code> || <code>Integrate[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], b*t]*BesselJ[\[Nu], c*t]*(t)^(1 - \[Mu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(b*c)^(\[Mu]- 1)*(Sin[\[Phi]])^(\[Mu]-Divide[1,2]),(2*Pi)^(Divide[1,2])* (a)^\[Mu]]*LegendreP[\[Nu]-Divide[1,2], Divide[1,2]- \[Mu], Cos[\[Phi]]]</code> || Translation Error || Translation Error || - || -
+|-
+| [https://dlmf.nist.gov/10.22.E72 10.22.E72] || [[Item:Q3446|<math>\int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1-\mu}\diff{t} = \frac{(bc)^{\mu-1}\sin@{(\mu-\nu)\cpi}(\sinh@@{\chi})^{\mu-\frac{1}{2}}}{(\frac{1}{2}\pi^{3})^{\frac{1}{2}}a^{\mu}}\expe^{(\mu-\frac{1}{2})\iunit\cpi}\assLegendreQ[\frac{1}{2}-\mu]{\nu-\frac{1}{2}}@{\cosh@@{\chi}}</math>]] || <code>int(BesselJ(mu, a*t)*BesselJ(nu, b*t)*BesselJ(nu, c*t)*(t)^(1 - mu), t = 0..infinity) = ((b*c)^(mu - 1)* sin((mu - nu)* Pi)*(sinh(chi))^(mu -(1)/(2)))/(((1)/(2)*(Pi)^(3))^((1)/(2))* (a)^(mu))*exp((mu -(1)/(2))* I*Pi)*LegendreQ(nu -(1)/(2), (1)/(2)- mu, cosh(chi))</code> || <code>Integrate[BesselJ[\[Mu], a*t]*BesselJ[\[Nu], b*t]*BesselJ[\[Nu], c*t]*(t)^(1 - \[Mu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(b*c)^(\[Mu]- 1)* Sin[(\[Mu]- \[Nu])* Pi]*(Sinh[\[Chi]])^(\[Mu]-Divide[1,2]),(Divide[1,2]*(Pi)^(3))^(Divide[1,2])* (a)^\[Mu]]*Exp[(\[Mu]-Divide[1,2])* I*Pi]*LegendreQ[\[Nu]-Divide[1,2], Divide[1,2]- \[Mu], 3, Cosh[\[Chi]]]</code> || Error || Aborted || - || Skip - No test values generated
+|-
+| [https://dlmf.nist.gov/10.23.E3 10.23.E3] || [[Item:Q3455|<math>\BesselJ{0}^{2}@{z}+2\sum_{k=1}^{\infty}\BesselJ{k}^{2}@{z} = 1</math>]] || <code>(BesselJ(0, z))^(2)+ 2*sum((BesselJ(k, z))^(2), k = 1..infinity) = 1</code> || <code>(BesselJ[0, z])^(2)+ 2*Sum[(BesselJ[k, z])^(2), {k, 1, Infinity}, GenerateConditions->None] == 1</code> || Aborted || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
 | [https://dlmf.nist.gov/10.23.E4 10.23.E4] || [[Item:Q3456|<math>\sum_{k=0}^{2n}(-1)^{k}\BesselJ{k}@{z}\BesselJ{2n-k}@{z}\\ +2\sum_{k=1}^{\infty}\BesselJ{k}@{z}\BesselJ{2n+k}@{z} = 0</math>]] || <code>sum((- 1)^(k)* BesselJ(k, z)*BesselJ(2*n - k, z), k = 0..2*n)+ 2*sum(BesselJ(k, z)*BesselJ(2*n + k, z), k = 1..infinity) = 0</code> || <code>Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[2*n - k, z], {k, 0, 2*n}, GenerateConditions->None]+ 2*Sum[BesselJ[k, z]*BesselJ[2*n + k, z], {k, 1, Infinity}, GenerateConditions->None] == 0</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.00727987412712798, -0.017853077134921347], Times[2.0, NSum[Times[BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[2.4034761502300195*^-4, -3.087748713313073*^-5], Times[2.0, NSum[Times[BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[4, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.23.E5 10.23.E5] || [[Item:Q3457|<math>\sum_{k=0}^{n}\BesselJ{k}@{z}\BesselJ{n-k}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{k}@{z}\BesselJ{n+k}@{z} = \BesselJ{n}@{2z}</math>]] || <code>sum(BesselJ(k, z)*BesselJ(n - k, z), k = 0..n)+ 2*sum((- 1)^(k)* BesselJ(k, z)*BesselJ(n + k, z), k = 1..infinity) = BesselJ(n, 2*z)</code> || <code>Sum[BesselJ[k, z]*BesselJ[n - k, z], {k, 0, n}, GenerateConditions->None]+ 2*Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[n + k, z], {k, 1, Infinity}, GenerateConditions->None] == BesselJ[n, 2*z]</code> || Error || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.024343533040476317, 0.10797471990649704], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[1, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.006069425709337772, 0.017711723121060452], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.23.E5 10.23.E5] || [[Item:Q3457|<math>\sum_{k=0}^{n}\BesselJ{k}@{z}\BesselJ{n-k}@{z}+2\sum_{k=1}^{\infty}(-1)^{k}\BesselJ{k}@{z}\BesselJ{n+k}@{z} = \BesselJ{n}@{2z}</math>]] || <code>sum(BesselJ(k, z)*BesselJ(n - k, z), k = 0..n)+ 2*sum((- 1)^(k)* BesselJ(k, z)*BesselJ(n + k, z), k = 1..infinity) = BesselJ(n, 2*z)</code> || <code>Sum[BesselJ[k, z]*BesselJ[n - k, z], {k, 0, n}, GenerateConditions->None]+ 2*Sum[(- 1)^(k)* BesselJ[k, z]*BesselJ[n + k, z], {k, 1, Infinity}, GenerateConditions->None] == BesselJ[n, 2*z]</code> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.024343533040476317, 0.10797471990649704], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[1, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.006069425709337772, 0.017711723121060452], Times[2.0, NSum[Times[Power[-1, k], BesselJ[k, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], BesselJ[Plus[2, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
 | [https://dlmf.nist.gov/10.23#Ex1 10.23#Ex1] || [[Item:Q3458|<math>w = \sqrt{u^{2}+v^{2}-2uv\cos@@{\alpha}}</math>]] || <code>w = sqrt((u)^(2)+ (v)^(2)- 2*u*v*cos(alpha))</code> || <code>w == Sqrt[(u)^(2)+ (v)^(2)- 2*u*v*Cos[\[Alpha]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.3146075610-.1816387601*I <- {alpha = 3/2, u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.680632965+.1843866439*I <- {alpha = 3/2, u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.3146075609842255, -0.18163876002333418] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Complex[0.4375091763619045, 0.252596040745477] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
@@ Line 419: / Line 499: @@
 | [https://dlmf.nist.gov/10.23#Ex3 10.23#Ex3] || [[Item:Q3460|<math>v\sin@@{\alpha} = w\sin@@{\chi}</math>]] || <code>v*sin(alpha) = w*sin(chi)</code> || <code>v*Sin[\[Alpha]] == w*Sin[\[Chi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.2887554391-.2231097873*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I}</code><br><code>1.585713279-.763530664e-1*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [294 / 300]<div class="mw-collapsible-content"><code>{Complex[0.2887554393029954, -0.22310978722682606] <- {Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.8740447527972026, 0.09051196331992012] <- {Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.23.E9 10.23.E9] || [[Item:Q3463|<math>e^{iv\cos@@{\alpha}} = \frac{\EulerGamma@{\nu}}{(\tfrac{1}{2}v)^{\nu}}\*\sum_{k=0}^{\infty}(\nu+k)i^{k}\BesselJ{\nu+k}@{v}\ultrasphpoly{\nu}{k}@{\cos@@{\alpha}}</math>]] || <code>exp(I*v*cos(alpha)) = (GAMMA(nu))/(((1)/(2)*v)^(nu))* sum((nu + k)* (I)^(k)* BesselJ(nu + k, v)*GegenbauerC(k, nu, cos(alpha)), k = 0..infinity)</code> || <code>Exp[I*v*Cos[\[Alpha]]] == Divide[Gamma[\[Nu]],(Divide[1,2]*v)^\[Nu]]* Sum[(\[Nu]+ k)* (I)^(k)* BesselJ[\[Nu]+ k, v]*GegenbauerC[k, \[Nu], Cos[\[Alpha]]], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.23.E9 10.23.E9] || [[Item:Q3463|<math>e^{iv\cos@@{\alpha}} = \frac{\EulerGamma@{\nu}}{(\tfrac{1}{2}v)^{\nu}}\*\sum_{k=0}^{\infty}(\nu+k)i^{k}\BesselJ{\nu+k}@{v}\ultrasphpoly{\nu}{k}@{\cos@@{\alpha}}</math>]] || <code>exp(I*v*cos(alpha)) = (GAMMA(nu))/(((1)/(2)*v)^(nu))* sum((nu + k)* (I)^(k)* BesselJ(nu + k, v)*GegenbauerC(k, nu, cos(alpha)), k = 0..infinity)</code> || <code>Exp[I*v*Cos[\[Alpha]]] == Divide[Gamma[\[Nu]],(Divide[1,2]*v)^\[Nu]]* Sum[(\[Nu]+ k)* (I)^(k)* BesselJ[\[Nu]+ k, v]*GegenbauerC[k, \[Nu], Cos[\[Alpha]]], {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Failure || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.23.E15 10.23.E15] || [[Item:Q3469|<math>(\tfrac{1}{2}z)^{\nu} = \sum_{k=0}^{\infty}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\BesselJ{\nu+2k}@{z}</math>]] || <code>((1)/(2)*z)^(nu) = sum(((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselJ(nu + 2*k, z), k = 0..infinity)</code> || <code>(Divide[1,2]*z)^\[Nu] == Sum[Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselJ[\[Nu]+ 2*k, z], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Successful || Skipped - Because timed out || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.23.E15 10.23.E15] || [[Item:Q3469|<math>(\tfrac{1}{2}z)^{\nu} = \sum_{k=0}^{\infty}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\BesselJ{\nu+2k}@{z}</math>]] || <code>((1)/(2)*z)^(nu) = sum(((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselJ(nu + 2*k, z), k = 0..infinity)</code> || <code>(Divide[1,2]*z)^\[Nu] == Sum[Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselJ[\[Nu]+ 2*k, z], {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Successful || Skipped - Because timed out || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.23.E16 10.23.E16] || [[Item:Q3470|<math>\BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}-\frac{4}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{\BesselJ{2k}@{z}}{k}</math>]] || <code>BesselY(0, z) = (2)/(Pi)*(ln((1)/(2)*z)+ gamma)* BesselJ(0, z)-(4)/(Pi)*sum((- 1)^(k)*(BesselJ(2*k, z))/(k), k = 1..infinity)</code> || <code>BesselY[0, z] == Divide[2,Pi]*(Log[Divide[1,2]*z]+ EulerGamma)* BesselJ[0, z]-Divide[4,Pi]*Sum[(- 1)^(k)*Divide[BesselJ[2*k, z],k], {k, 1, Infinity}, GenerateConditions->None]</code> || Error || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.23.E16 10.23.E16] || [[Item:Q3470|<math>\BesselY{0}@{z} = \frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\BesselJ{0}@{z}-\frac{4}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{\BesselJ{2k}@{z}}{k}</math>]] || <code>BesselY(0, z) = (2)/(Pi)*(ln((1)/(2)*z)+ gamma)* BesselJ(0, z)-(4)/(Pi)*sum((- 1)^(k)*(BesselJ(2*k, z))/(k), k = 1..infinity)</code> || <code>BesselY[0, z] == Divide[2,Pi]*(Log[Divide[1,2]*z]+ EulerGamma)* BesselJ[0, z]-Divide[4,Pi]*Sum[(- 1)^(k)*Divide[BesselJ[2*k, z],k], {k, 1, Infinity}, GenerateConditions->None]</code> || Aborted || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.23.E17 10.23.E17] || [[Item:Q3471|<math>\BesselY{n}@{z} = -\frac{n!(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}\BesselJ{k}@{z}}{k!(n-k)}+\frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\BesselJ{n}@{z}-\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{(n+2k)\BesselJ{n+2k}@{z}}{k(n+k)}</math>]] || <code>BesselY(n, z) = -(factorial(n)*((1)/(2)*z)^(- n))/(Pi)*sum((((1)/(2)*z)^(k)* BesselJ(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(2)/(Pi)*(ln((1)/(2)*z)- Psi(n + 1))* BesselJ(n, z)-(2)/(Pi)*sum((- 1)^(k)*((n + 2*k)* BesselJ(n + 2*k, z))/(k*(n + k)), k = 1..infinity)</code> || <code>BesselY[n, z] == -Divide[(n)!*(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(Divide[1,2]*z)^(k)* BesselJ[k, z],(k)!*(n - k)], {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselJ[n, z]-Divide[2,Pi]*Sum[(- 1)^(k)*Divide[(n + 2*k)* BesselJ[n + 2*k, z],k*(n + k)], {k, 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [16 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.41373222494160333, 0.38808044477324316], Times[Complex[0.5513288954217921, -0.31830988618379064], DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[Times[-1, ], 1], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], []], Times[Plus[4, Times[12, ], Times[12, Power[, 2]], Times[4, Power[, 3]], Times[-4, 1], Times[-8, , 1], Times[-4, Power[, 2], 1], Times[, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-1, 1, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], [Plus[1, ]]], Times[4, Plus[1, ], Plus[-5, Times[-6, ], Times[-2, Power[, 2]], Times[3, 1], Times[2, , 1]], [Plus[2, ]]], Times[-4, Plus[1, ], Plus[2, ], Plus[-2, Times[-1, ], 1], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[1, 2], Power[Plus[-1, 1], -1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], BesselJ[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.6198631863998064, 5.383408526303685], Times[Complex[0.0, -15.278874536821952], DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-1, Power[-1, Rational[1, 3]], Plus[-3, ], []], Times[Plus[-8, Times[-3, Power[-1, Rational[1, 3]]], Times[-12, ], Times[Power[-1, Rational[1, 3]], ], Times[4, Power[, 3]]], [Plus[1, ]]], Times[-8, Plus[1, ], Plus[-2, Power[, 2]], [Plus[2, ]]], Times[4, Plus[-1, ], Plus[1, ], Plus[2, ], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Rational[1, 3], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Rational[1, 3], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[1, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], BesselJ[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][3.0]]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.23.E17 10.23.E17] || [[Item:Q3471|<math>\BesselY{n}@{z} = -\frac{n!(\tfrac{1}{2}z)^{-n}}{\pi}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}\BesselJ{k}@{z}}{k!(n-k)}+\frac{2}{\pi}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\BesselJ{n}@{z}-\frac{2}{\pi}\sum_{k=1}^{\infty}(-1)^{k}\frac{(n+2k)\BesselJ{n+2k}@{z}}{k(n+k)}</math>]] || <code>BesselY(n, z) = -(factorial(n)*((1)/(2)*z)^(- n))/(Pi)*sum((((1)/(2)*z)^(k)* BesselJ(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(2)/(Pi)*(ln((1)/(2)*z)- Psi(n + 1))* BesselJ(n, z)-(2)/(Pi)*sum((- 1)^(k)*((n + 2*k)* BesselJ(n + 2*k, z))/(k*(n + k)), k = 1..infinity)</code> || <code>BesselY[n, z] == -Divide[(n)!*(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(Divide[1,2]*z)^(k)* BesselJ[k, z],(k)!*(n - k)], {k, 0, n - 1}, GenerateConditions->None]+Divide[2,Pi]*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselJ[n, z]-Divide[2,Pi]*Sum[(- 1)^(k)*Divide[(n + 2*k)* BesselJ[n + 2*k, z],k*(n + k)], {k, 1, Infinity}, GenerateConditions->None]</code> || Aborted || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [16 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.41373222494160333, 0.38808044477324316], Times[Complex[0.5513288954217921, -0.31830988618379064], DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[Times[-1, ], 1], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2], []], Times[Plus[4, Times[12, ], Times[12, Power[, 2]], Times[4, Power[, 3]], Times[-4, 1], Times[-8, , 1], Times[-4, Power[, 2], 1], Times[, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[-1, 1, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]]], [Plus[1, ]]], Times[4, Plus[1, ], Plus[-5, Times[-6, ], Times[-2, Power[, 2]], Times[3, 1], Times[2, , 1]], [Plus[2, ]]], Times[-4, Plus[1, ], Plus[2, ], Plus[-2, Times[-1, ], 1], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Power[1, -1], BesselJ[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[1, 2], Power[Plus[-1, 1],</div></div>
 |-
 | [https://dlmf.nist.gov/10.24.E1 10.24.E1] || [[Item:Q3476|<math>x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(x^{2}+\nu^{2})w = 0</math>]] || <code>(x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((x)^(2)+ (nu)^(2))* w = 0</code> || <code>(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+((x)^(2)+ \[Nu]^(2))* w == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.948557159+2.125000000*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>.2165063513+1.125000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.9485571585149875, 2.125] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.948557158514987, 0.12499999999999989] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 482: / Line 562: @@
 |-
 | [https://dlmf.nist.gov/10.29#Ex6 10.29#Ex6] || [[Item:Q3509|<math>\modBesselK{0}'@{z} = -\modBesselK{1}@{z}</math>]] || <code>diff( BesselK(0, z), z$(1) ) = - BesselK(1, z)</code> || <code>D[BesselK[0, z], {z, 1}] == - BesselK[1, z]</code> || Successful || Successful || - || Successful [Tested: 7]
+|-
+| [https://dlmf.nist.gov/10.31.E1 10.31.E1] || [[Item:Q3518|<math>\modBesselK{n}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}(-\tfrac{1}{4}z^{2})^{k}+(-1)^{n+1}\ln@{\tfrac{1}{2}z}\modBesselI{n}@{z}+(-1)^{n}\tfrac{1}{2}(\tfrac{1}{2}z)^{n}\sum_{k=0}^{\infty}\left(\digamma@{k+1}+\digamma@{n+k+1}\right)\frac{(\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!}</math>]] || <code>BesselK(n, z) = (1)/(2)*((1)/(2)*z)^(- n)* sum((factorial(n - k - 1))/(factorial(k))*(-(1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(- 1)^(n + 1)* ln((1)/(2)*z)*BesselI(n, z)+(- 1)^(n)*(1)/(2)*((1)/(2)*z)^(n)* sum((Psi(k + 1)+ Psi(n + k + 1))*(((1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity)</code> || <code>BesselK[n, z] == Divide[1,2]*(Divide[1,2]*z)^(- n)* Sum[Divide[(n - k - 1)!,(k)!]*(-Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n + 1)* Log[Divide[1,2]*z]*BesselI[n, z]+(- 1)^(n)*Divide[1,2]*(Divide[1,2]*z)^(n)* Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Aborted || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><code>{Plus[0.6666666666666666, Times[-0.6666666666666666, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Power[1.5, 2]], [Plus[2, ]]], Times[-1, Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equal[[2], Plus[1, Times[-4, Power[1.5, -2]]]], Equal[[3], Plus[Rational[1, 2], Times[16, Power[1.5, -4], Plus[2, Times[Rational[-1, 4], Power[1.5, 2]]]]]], Equal[[4], Times[Rational[-32, 3], Power[1.5, -6], Plus[3, Times[Rational[-1, 4], Power[1.5, 2]]], Plus[12, Times[Rational[1, 16], Power[1.5, 4]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, 1.5]}</code><br><code>Plus[0.38888888888888906, Times[0.5, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[-4, []], Times[Plus[12, Times[8, ]], [Plus[1, ]]], Times[Plus[-16, Times[-16, ], Times[-4, Power[, 2]], Power[1.5, 2]], [Plus[2, ]]], Times[-1, Plus[2, ], Power[1.5, 2], [Plus[3, ]]]], 0], Equal[[1], 1], Equ</div></div>
 |-
 | [https://dlmf.nist.gov/10.31.E2 10.31.E2] || [[Item:Q3519|<math>\modBesselK{0}@{z} = -\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\modBesselI{0}@{z}+\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}+(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}+\dotsi</math>]] || <code>BesselK(0, z) = -(ln((1)/(2)*z)+ gamma)* BesselI(0, z)+((1)/(4)*(z)^(2))/((factorial(1))^(2))+(1 +(1)/(2))*(((1)/(4)*(z)^(2))^(2))/((factorial(2))^(2))+(1 +(1)/(2)+(1)/(3))*(((1)/(4)*(z)^(2))^(3))/((factorial(3))^(2))+ ..</code> || <code>BesselK[0, z] == -(Log[Divide[1,2]*z]+ EulerGamma)* BesselI[0, z]+Divide[Divide[1,4]*(z)^(2),((1)!)^(2)]+(1 +Divide[1,2])*Divide[(Divide[1,4]*(z)^(2))^(2),((2)!)^(2)]+(1 +Divide[1,2]+Divide[1,3])*Divide[(Divide[1,4]*(z)^(2))^(3),((3)!)^(2)]+ \[Ellipsis]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[-6.985673039111573*^-6, -1.2369744460005716*^-5], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-7.140527721077872*^-6, -1.2101549865001227*^-5], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 495: / Line 577: @@
 | [https://dlmf.nist.gov/10.32.E1 10.32.E1] || [[Item:Q3521|<math>\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\diff{\theta} = \frac{1}{\pi}\int_{0}^{\pi}\cosh@{z\cos@@{\theta}}\diff{\theta}</math>]] || <code>(1)/(Pi)*int(exp(- z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi)</code> || <code>Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[Cosh[z*Cos[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]] || <code>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</code> || <code>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]] || <code>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</code> || <code>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
+|-
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]] || <code>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</code> || <code>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
+|-
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}</math>]] || <code>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(+ z*t), t = - 1..1)</code> || <code>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 35]
+|-
+| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{- zt}\diff{t}</math>]] || <code>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(- z*t), t = - 1..1)</code> || <code>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[- z*t], {t, - 1, 1}, GenerateConditions->None]</code> || Error || Aborted || Skip - symbolical successful subtest || Successful [Tested: 35]
+|-
+| [https://dlmf.nist.gov/10.32.E3 10.32.E3] || [[Item:Q3523|<math>\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</math>]] || <code>BesselI(n, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(n*theta), theta = 0..Pi)</code> || <code>BesselI[n, z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 21] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\modBesselI{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{- z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta}</math>]] || <code>BesselI(nu, z) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)</code> || <code>BesselI[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E4 10.32.E4] || [[Item:Q3524|<math>\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}</math>]] || <code>BesselI(nu, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity)</code> || <code>BesselI[\[Nu], z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[\[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Cosh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E2 10.32.E2] || [[Item:Q3522|<math>\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}(\sin@@{\theta})^{2\nu}\diff{\theta} = \frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\EulerGamma@{\nu+\frac{1}{2}}}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{+ zt}\diff{t}</math>]] || <code>(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(exp(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) = (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* exp(+ z*t), t = - 1..1)</code> || <code>Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[+ z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}, GenerateConditions->None] == Divide[(Divide[1,2]*z)^\[Nu],(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Exp[+ z*t], {t, - 1, 1}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Successful [Tested: 35]
+| [https://dlmf.nist.gov/10.32.E5 10.32.E5] || [[Item:Q3525|<math>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{+ z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</math>]] || <code>BesselK(0, z) = -(1)/(Pi)*int(exp(+ z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi)</code> || <code>BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E3 10.32.E3] || [[Item:Q3523|<math>\modBesselI{n}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{n\theta}\diff{\theta}</math>]] || <code>BesselI(n, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(n*theta), theta = 0..Pi)</code> || <code>BesselI[n, z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 21] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E5 10.32.E5] || [[Item:Q3525|<math>\modBesselK{0}@{z} = -\frac{1}{\pi}\int_{0}^{\pi}e^{- z\cos@@{\theta}}\left(\EulerConstant+\ln@{2z(\sin@@{\theta})^{2}}\right)\diff{\theta}</math>]] || <code>BesselK(0, z) = -(1)/(Pi)*int(exp(- z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi)</code> || <code>BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E4 10.32.E4] || [[Item:Q3524|<math>\modBesselI{\nu}@{z} = \frac{1}{\pi}\int_{0}^{\pi}e^{z\cos@@{\theta}}\cos@{\nu\theta}\diff{\theta}-\frac{\sin@{\nu\pi}}{\pi}\int_{0}^{\infty}e^{-z\cosh@@{t}-\nu t}\diff{t}</math>]] || <code>BesselI(nu, z) = (1)/(Pi)*int(exp(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity)</code> || <code>BesselI[\[Nu], z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[Theta]]]*Cos[\[Nu]*\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Cosh[t]- \[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || [[Item:Q3526|<math>\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}</math>]] || <code>BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity)</code> || <code>BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || [[Item:Q3526|<math>\modBesselK{0}@{x} = \int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t}</math>]] || <code>BesselK(0, x) = int(cos(x*sinh(t)), t = 0..infinity)</code> || <code>BesselK[0, x] == Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || [[Item:Q3526|<math>\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}</math>]] || <code>int(cos(x*sinh(t)), t = 0..infinity) = int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity)</code> || <code>Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[x*t],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E6 10.32.E6] || [[Item:Q3526|<math>\int_{0}^{\infty}\cos@{x\sinh@@{t}}\diff{t} = \int_{0}^{\infty}\frac{\cos@{xt}}{\sqrt{t^{2}+1}}\diff{t}</math>]] || <code>int(cos(x*sinh(t)), t = 0..infinity) = int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity)</code> || <code>Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[x*t],Sqrt[(t)^(2)+ 1]], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || [[Item:Q3527|<math>\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselK(nu, x) = sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity)</code> || <code>BesselK[\[Nu], x] == Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || [[Item:Q3527|<math>\modBesselK{\nu}@{x} = \sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselK(nu, x) = sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity)</code> || <code>BesselK[\[Nu], x] == Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || [[Item:Q3527|<math>\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}</math>]] || <code>sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) = csc((1)/(2)*nu*Pi)*int(sin(x*sinh(t))*sinh(nu*t), t = 0..infinity)</code> || <code>Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]*\[Nu]*Pi]*Integrate[Sin[x*Sinh[t]]*Sinh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E7 10.32.E7] || [[Item:Q3527|<math>\sec@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\cos@{x\sinh@@{t}}\cosh@{\nu t}\diff{t} = \csc@{\tfrac{1}{2}\nu\pi}\int_{0}^{\infty}\sin@{x\sinh@@{t}}\sinh@{\nu t}\diff{t}</math>]] || <code>sec((1)/(2)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) = csc((1)/(2)*nu*Pi)*int(sin(x*sinh(t))*sinh(nu*t), t = 0..infinity)</code> || <code>Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None] == Csc[Divide[1,2]*\[Nu]*Pi]*Integrate[Sin[x*Sinh[t]]*Sinh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || [[Item:Q3528|<math>\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}</math>]] || <code>BesselK(nu, z) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity)</code> || <code>BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || [[Item:Q3528|<math>\modBesselK{\nu}@{z} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t}</math>]] || <code>BesselK(nu, z) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity)</code> || <code>BesselK[\[Nu], z] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E8 10.32.E8] || [[Item:Q3528|<math>\frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{0}^{\infty}e^{-z\cosh@@{t}}(\sinh@@{t})^{2\nu}\diff{t} = \frac{\pi^{\frac{1}{2}}(\frac{1}{2}z)^{\nu}}{\EulerGamma@{\nu+\frac{1}{2}}}\int_{1}^{\infty}e^{-zt}(t^{2}-1)^{\nu-\frac{1}{2}}\diff{t}</math>]] || <code>((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity) = ((Pi)^((1)/(2))*((1)/(2)*z)^(nu))/(GAMMA(nu +(1)/(2)))*int(exp(- z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1..infinity)</code> || <code>Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*Cosh[t]]*(Sinh[t])^(2*\[Nu]), {t, 0, Infinity}, GenerateConditions->None] == Divide[(Pi)^(Divide[1,2])*(Divide[1,2]*z)^\[Nu],Gamma[\[Nu]+Divide[1,2]]]*Integrate[Exp[- z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1, Infinity}, GenerateConditions->None]</code> || Error || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E9 10.32.E9] || [[Item:Q3529|<math>\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselK(nu, z) = int(exp(- z*cosh(t))*cosh(nu*t), t = 0..infinity)</code> || <code>BesselK[\[Nu], z] == Integrate[Exp[- z*Cosh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E9 10.32.E9] || [[Item:Q3529|<math>\modBesselK{\nu}@{z} = \int_{0}^{\infty}e^{-z\cosh@@{t}}\cosh@{\nu t}\diff{t}</math>]] || <code>BesselK(nu, z) = int(exp(- z*cosh(t))*cosh(nu*t), t = 0..infinity)</code> || <code>BesselK[\[Nu], z] == Integrate[Exp[- z*Cosh[t]]*Cosh[\[Nu]*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.32.E10 10.32.E10] || [[Item:Q3530|<math>\modBesselK{\nu}@{z} = \tfrac{1}{2}(\tfrac{1}{2}z)^{\nu}\int_{0}^{\infty}\exp@{-t-\frac{z^{2}}{4t}}\frac{\diff{t}}{t^{\nu+1}}</math>]] || <code>BesselK(nu, z) = (1)/(2)*((1)/(2)*z)^(nu)* int(exp(- t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = 0..infinity)</code> || <code>BesselK[\[Nu], z] == Divide[1,2]*(Divide[1,2]*z)^\[Nu]* Integrate[Exp[- t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 40]
+|-
+| [https://dlmf.nist.gov/10.32.E11 10.32.E11] || [[Item:Q3531|<math>\modBesselK{\nu}@{xz} = \frac{\EulerGamma@{\nu+\frac{1}{2}}(2z)^{\nu}}{\pi^{\frac{1}{2}}x^{\nu}}\int_{0}^{\infty}\frac{\cos@{xt}\diff{t}}{(t^{2}+z^{2})^{\nu+\frac{1}{2}}}</math>]] || <code>BesselK(nu, x*(x + y*I)) = (GAMMA(nu +(1)/(2))*(2*(x + y*I))^(nu))/((Pi)^((1)/(2))* (x)^(nu))*int((cos(x*t))/(((t)^(2)+(x + y*I)^(2))^(nu +(1)/(2))), t = 0..infinity)</code> || <code>BesselK[\[Nu], x*(x + y*I)] == Divide[Gamma[\[Nu]+Divide[1,2]]*(2*(x + y*I))^\[Nu],(Pi)^(Divide[1,2])* (x)^\[Nu]]*Integrate[Divide[Cos[x*t],((t)^(2)+(x + y*I)^(2))^(\[Nu]+Divide[1,2])], {t, 0, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.32.E12 10.32.E12] || [[Item:Q3532|<math>\modBesselI{\nu}@{z} = \frac{1}{2\pi i}\int_{\infty-i\pi}^{\infty+i\pi}e^{z\cosh@@{t}-\nu t}\diff{t}</math>]] || <code>BesselI(nu, z) = (1)/(2*Pi*I)*int(exp(z*cosh(t)- nu*t), t = infinity - I*Pi..infinity + I*Pi)</code> || <code>BesselI[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Cosh[t]- \[Nu]*t], {t, Infinity - I*Pi, Infinity + I*Pi}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [50 / 50]<div class="mw-collapsible-content"><code>{Complex[0.5303418993681409, 0.010453999760907294] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.7664848208906112, 0.1468422559210476] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.32.E13 10.32.E13] || [[Item:Q3533|<math>\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}</math>]] || <code>BesselK(nu, z) = (((1)/(2)*z)^(nu))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>BesselK[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],4*Pi*I]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.5663982443-.3181066824*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.434992817-2.759712160*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E13 10.32.E13] || [[Item:Q3533|<math>\modBesselK{\nu}@{z} = \frac{(\frac{1}{2}z)^{\nu}}{4\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{t}\EulerGamma@{t-\nu}(\tfrac{1}{2}z)^{-2t}\diff{t}</math>]] || <code>BesselK(nu, z) = (((1)/(2)*z)^(nu))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>BesselK[\[Nu], z] == Divide[(Divide[1,2]*z)^\[Nu],4*Pi*I]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.5663982443-.3181066824*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.434992817-2.759712160*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.32.E14 10.32.E14] || [[Item:Q3534|<math>\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}</math>]] || <code>BesselK(nu, z) = (1)/(2*(Pi)^(2)* I)*((Pi)/(2*z))^((1)/(2))* exp(- z)*cos(nu*Pi)* int(GAMMA(t)*GAMMA((1)/(2)- t - nu)*GAMMA((1)/(2)- t + nu)*(2*z)^(t), t = - I*infinity..I*infinity)</code> || <code>BesselK[\[Nu], z] == Divide[1,2*(Pi)^(2)* I]*(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*Cos[\[Nu]*Pi]* Integrate[Gamma[t]*Gamma[Divide[1,2]- t - \[Nu]]*Gamma[Divide[1,2]- t + \[Nu]]*(2*z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.32.E15 10.32.E15] || [[Item:Q3535|<math>\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</math>]] || <code>BesselI(mu, z)*BesselI(nu, z) = (2)/(Pi)*int(BesselI(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..(1)/(2)*Pi)</code> || <code>BesselI[\[Mu], z]*BesselI[\[Nu], z] == Divide[2,Pi]*Integrate[BesselI[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.32.E16 10.32.E16] || [[Item:Q3536|<math>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu+\nu}@{2x\sinh@@{t}}e^{(-\mu+\nu)t}\diff{t}</math>]] || <code>BesselI(mu, x)*BesselK(nu, x) = int(BesselJ(mu + nu, 2*x*sinh(t))*exp((- mu + nu)* t), t = 0..infinity)</code> || <code>BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]+ \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]+ \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.32.E16 10.32.E16] || [[Item:Q3536|<math>\modBesselI{\mu}@{x}\modBesselK{\nu}@{x} = \int_{0}^{\infty}\BesselJ{\mu-\nu}@{2x\sinh@@{t}}e^{(-\mu-\nu)t}\diff{t}</math>]] || <code>BesselI(mu, x)*BesselK(nu, x) = int(BesselJ(mu - nu, 2*x*sinh(t))*exp((- mu - nu)* t), t = 0..infinity)</code> || <code>BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]- \[Nu], 2*x*Sinh[t]]*Exp[(- \[Mu]- \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E14 10.32.E14] || [[Item:Q3534|<math>\modBesselK{\nu}@{z} = \frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t}</math>]] || <code>BesselK(nu, z) = (1)/(2*(Pi)^(2)* I)*((Pi)/(2*z))^((1)/(2))* exp(- z)*cos(nu*Pi)* int(GAMMA(t)*GAMMA((1)/(2)- t - nu)*GAMMA((1)/(2)- t + nu)*(2*z)^(t), t = - I*infinity..I*infinity)</code> || <code>BesselK[\[Nu], z] == Divide[1,2*(Pi)^(2)* I]*(Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*Cos[\[Nu]*Pi]* Integrate[Gamma[t]*Gamma[Divide[1,2]- t - \[Nu]]*Gamma[Divide[1,2]- t + \[Nu]]*(2*z)^(t), {t, - I*Infinity, I*Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || [[Item:Q3537|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}</math>]] || <code>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)* t), t = 0..infinity)</code> || <code>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]- \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E15 10.32.E15] || [[Item:Q3535|<math>\modBesselI{\mu}@{z}\modBesselI{\nu}@{z} = \frac{2}{\pi}\int_{0}^{\frac{1}{2}\pi}\modBesselI{\mu+\nu}@{2z\cos@@{\theta}}\cos@{(\mu-\nu)\theta}\diff{\theta}</math>]] || <code>BesselI(mu, z)*BesselI(nu, z) = (2)/(Pi)*int(BesselI(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..(1)/(2)*Pi)</code> || <code>BesselI[\[Mu], z]*BesselI[\[Nu], z] == Divide[2,Pi]*Integrate[BesselI[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || [[Item:Q3537|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}</math>]] || <code>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)* t), t = 0..infinity)</code> || <code>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]+ \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || [[Item:Q3537|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu+\nu}@{2z\cosh@@{t}}\cosh@{(\mu-\nu)t}\diff{t}</math>]] || <code>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)* t), t = 0..infinity)</code> || <code>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]- \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E18 10.32.E18] || [[Item:Q3538|<math>\modBesselK{\nu}@{z}\modBesselK{\nu}@{\zeta} = \frac{1}{2}\int_{0}^{\infty}\exp@{-\frac{t}{2}-\frac{z^{2}+\zeta^{2}}{2t}}\modBesselK{\nu}\left(\frac{z\zeta}{t}\right)\frac{\diff{t}}{t}</math>]] || <code>BesselK(nu, z)*BesselK(nu, zeta) = (1)/(2)*int(exp(-(t)/(2)-((z)^(2)+ (zeta)^(2))/(2*t))*BesselK(nu, ((z*zeta)/(t))*)*(1)/(t), t = 0..infinity)</code> || <code>BesselK[\[Nu], z]*BesselK[\[Nu], \[Zeta]] == Divide[1,2]*Integrate[Exp[-Divide[t,2]-Divide[(z)^(2)+ \[Zeta]^(2),2*t]]*BesselK[\[Nu], (Divide[z*\[Zeta],t])*]*Divide[1,t], {t, 0, Infinity}, GenerateConditions->None]</code> || Translation Error || Translation Error || - || -
 |-
-| [https://dlmf.nist.gov/10.32.E17 10.32.E17] || [[Item:Q3537|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = 2\int_{0}^{\infty}\modBesselK{\mu-\nu}@{2z\cosh@@{t}}\cosh@{(\mu+\nu)t}\diff{t}</math>]] || <code>BesselK(mu, z)*BesselK(nu, z) = 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)* t), t = 0..infinity)</code> || <code>BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[t]]*Cosh[(\[Mu]+ \[Nu])* t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.32.E19 10.32.E19] || [[Item:Q3539|<math>\modBesselK{\mu}@{z}\modBesselK{\nu}@{z} = \frac{1}{8\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{t+\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t+\frac{1}{2}\mu-\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu+\frac{1}{2}\nu}\EulerGamma@{t-\frac{1}{2}\mu-\frac{1}{2}\nu}}{\EulerGamma@{2t}}(\tfrac{1}{2}z)^{-2t}\diff{t}</math>]] || <code>BesselK(mu, z)*BesselK(nu, z) = (1)/(8*Pi*I)*int((GAMMA(t +(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t +(1)/(2)*mu -(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu +(1)/(2)*nu)*GAMMA(t -(1)/(2)*mu -(1)/(2)*nu))/(GAMMA(2*t))*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity)</code> || <code>BesselK[\[Mu], z]*BesselK[\[Nu], z] == Divide[1,8*Pi*I]*Integrate[Divide[Gamma[t +Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t +Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]*Gamma[t -Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]],Gamma[2*t]]*(Divide[1,2]*z)^(- 2*t), {t, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skip - No test values generated
 |-
 |}

Results of Bessel Functions I: Difference between revisions

Revision as of 19:51, 15 October 2020

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