Results of Bessel Functions I

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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)])+ z*diff(w, z)+((z)^(2)- (nu)^(2))* w = 0 (z)^(2)* D[w, {z, 2}]+ z*D[w, z]+((z)^(2)- \[Nu]^(2))* w == 0 Failure Failure
Failed [217 / 300]
217/300]: [[-.8660254040e-9-2.000000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
-.8660254040e-9-2.000000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(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(nu*Pi)- 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)/(2*I)*(HankelH1(nu, z)- HankelH2(nu, z)) BesselY[\[Nu], z] == Divide[1,2*I]*(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(nu*Pi)*(BesselY(- nu, z)- BesselY(nu, z)*cos(nu*Pi)) 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(nu*Pi*I)*HankelH1(nu, z) HankelH1[- \[Nu], z] == Exp[\[Nu]*Pi*I]*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(- nu*Pi*I)*HankelH2(nu, z) HankelH2[- \[Nu], z] == Exp[- \[Nu]*Pi*I]*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) = I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z)) HankelH1[\[Nu], z] == I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*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)} I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z)) = csc(nu*Pi)*(BesselY(- nu, z)- exp(- nu*Pi*I)*BesselY(nu, z)) I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z]) == Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[- \[Nu]*Pi*I]*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) = I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z)) HankelH2[\[Nu], z] == I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*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)} I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z)) = csc(nu*Pi)*(BesselY(- nu, z)- exp(nu*Pi*I)*BesselY(nu, z)) I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z]) == Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[\[Nu]*Pi*I]*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) = - 2*sin(nu*Pi)/(Pi*z) BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z] == - 2*Sin[\[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) = 2*I/(Pi*z) BesselJ[\[Nu]+ 1, z]*HankelH1[\[Nu], z]- BesselJ[\[Nu], z]*HankelH1[\[Nu]+ 1, z] == 2*I/(Pi*z) 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) = - 2*I/(Pi*z) BesselJ[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- BesselJ[\[Nu], z]*HankelH2[\[Nu]+ 1, z] == - 2*I/(Pi*z) 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) = - 4*I/(Pi*z) HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z] == - 4*I/(Pi*z) 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) = (2*nu/ 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] = -(2*nu)/(a)*q[nu]-(2*nu)/(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))/(a*b)*p[nu] Subscript[s, \[Nu]] == Divide[1,2]*Subscript[p, \[Nu]+ 1]+Divide[1,2]*Subscript[p, \[Nu]- 1]-Divide[\[Nu]^(2),a*b]*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(z*sin(theta)), theta = 0..Pi) BesselJ[0, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[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(z*sin(theta)), theta = 0..Pi) = (1)/(Pi)*int(cos(z*cos(theta)), theta = 0..Pi) 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] 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(z*sin(theta)- n*theta), theta = 0..Pi) BesselJ[n, z] == Divide[1,Pi]*Integrate[Cos[z*Sin[\[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(z*sin(theta)- n*theta), theta = 0..Pi) = ((I)^(- n))/(Pi)*int(exp(I*z*cos(theta))*cos(n*theta), theta = 0..Pi) 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] 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(z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..(1)/(2)*Pi) 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] 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(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) 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] 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(z*cos(theta))*(sin(theta))^(2*nu), 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[z*Cos[\[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(z*t), t = 0..1)- int(exp(- z*t)*(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[z*t], {t, 0, 1}, GenerateConditions->None]- Integrate[Exp[- z*t]*(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(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*sinh(t)- nu*t), t = 0..infinity) 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] 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(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) 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] 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(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) BesselJ[\[Nu], x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[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(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) BesselY[\[Nu], x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[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(x*cosh(t)), t = 0..infinity) BesselJ[0, x] == Divide[2,Pi]*Integrate[Sin[x*Cosh[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(x*cosh(t)), t = 0..infinity) BesselY[0, x] == -Divide[2,Pi]*Integrate[Cos[x*Cosh[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)*nu*Pi*I))/(Pi*I)*int(exp(I*z*cosh(t)- nu*t), t = - infinity..infinity) 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] 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)*nu*Pi*I))/(Pi*I)*int(exp(- I*z*cosh(t)- nu*t), t = - infinity..infinity) 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] 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(x*t))/(((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[x*t],((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(x*t))/(((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[x*t],((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(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) (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] 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(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) (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] 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)/(Pi*I)*exp(-(1)/(2)*nu*Pi*I)*int(exp(I*z*cosh(t)+ I*zeta*sinh(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,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] 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)/(Pi*I)*exp((1)/(2)*nu*Pi*I)*int(exp(- I*z*cosh(t)- I*zeta*sinh(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,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] 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)/(2*Pi*I)*int(exp(z*sinh(t)- nu*t), t = infinity - Pi*I..infinity + Pi*I) BesselJ[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, Infinity - Pi*I, 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)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity + Pi*I) HankelH1[\[Nu], z] == Divide[1,Pi*I]*Integrate[Exp[z*Sinh[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)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity - Pi*I) HankelH2[\[Nu], z] == -Divide[1,Pi*I]*Integrate[Exp[z*Sinh[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))/(2*Pi*I)*int(exp(t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = - infinity..(0 +)) 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] 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(z*t)*((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[z*t]*((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(I*z*t)*((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[I*z*t]*((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(- I*z*t)*((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[- I*z*t]*((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)/(2*Pi*I)*int((GAMMA(- t)*((1)/(2)*x)^(nu + 2*t))/(GAMMA(nu + t + 1)), t = - I*infinity..I*infinity) 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] 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)/(2*Pi*I)*int((GAMMA(t))/(GAMMA(nu - t + 1))*((1)/(2)*z)^(nu - 2*t), t = - infinity - I*c..- infinity + I*c) 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] 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)*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) 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] Failure Aborted
Failed [120 / 120]
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}
-.8661908042+.2691615148*I <- {c = -3/2, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(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)*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) 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] Failure Aborted
Failed [120 / 120]
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)}
-.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}
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, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..Pi/ 2) 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] 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(2*nu, 2*(z*zeta)^((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)/(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) 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] 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)/(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) 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] 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(2*nu*t)*BesselK(0, 2*z*sinh(t)), t = 0..infinity) (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] 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, z*exp(m*Pi*I)) = exp(m*nu*Pi*I)*BesselJ(nu, z) BesselJ[\[Nu], z*Exp[m*Pi*I]] == Exp[m*\[Nu]*Pi*I]*BesselJ[\[Nu], z] Failure Failure
Failed [132 / 210]
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}
.4256613630-.5580360922e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = exp(- m*nu*Pi*I)*BesselY(nu, z)+ 2*I*sin(m*nu*Pi)*cot(nu*Pi)*BesselJ(nu, z) BesselY[\[Nu], z*Exp[m*Pi*I]] == Exp[- m*\[Nu]*Pi*I]*BesselY[\[Nu], z]+ 2*I*Sin[m*\[Nu]*Pi]*Cot[\[Nu]*Pi]*BesselJ[\[Nu], z] Failure Failure
Failed [170 / 210]
170/210]: [[-4.492502702+3.271310776*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}
19.72399963+2.416868418*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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(nu*Pi)*HankelH1(nu, z*exp(m*Pi*I)) = - sin((m - 1)* nu*Pi)*HankelH1(nu, z)- exp(- nu*Pi*I)*sin(m*nu*Pi)*HankelH2(nu, z) Sin[\[Nu]*Pi]*HankelH1[\[Nu], z*Exp[m*Pi*I]] == - Sin[(m - 1)* \[Nu]*Pi]*HankelH1[\[Nu], z]- Exp[- \[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH2[\[Nu], z] Failure Failure
Failed [132 / 210]
132/210]: [[-16.06107638+5.815014709*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}
39.27071892+24.34608468*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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(nu*Pi)*HankelH2(nu, z*exp(m*Pi*I)) = exp(nu*Pi*I)*sin(m*nu*Pi)*HankelH1(nu, z)+ sin((m + 1)* nu*Pi)*HankelH2(nu, z) Sin[\[Nu]*Pi]*HankelH2[\[Nu], z*Exp[m*Pi*I]] == Exp[\[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH1[\[Nu], z]+ Sin[(m + 1)* \[Nu]*Pi]*HankelH2[\[Nu], z] Failure Failure
Failed [132 / 210]
132/210]: [[9.518923666+1.283901315*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}
-38.63237633-26.24866521*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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, z*exp(Pi*I)) = - exp(- nu*Pi*I)*HankelH2(nu, z) HankelH1[\[Nu], z*Exp[Pi*I]] == - Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z] Failure Failure
Failed [20 / 70]
20/70]: [[-5.249915228-5.084103922*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
-3.129030441-5.176244122*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(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, z*exp(- Pi*I)) = - exp(nu*Pi*I)*HankelH1(nu, z) HankelH2[\[Nu], z*Exp[- Pi*I]] == - Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z] Failure Failure
Failed [50 / 70]
50/70]: [[1.033334476+.7163604616*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}
1.427918302+.5187414665*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}
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, z*exp(m*Pi*I)) = (- 1)^(m*n)*(BesselY(n, z)+ 2*I*m*BesselJ(n, z)) BesselY[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)*(BesselY[n, z]+ 2*I*m*BesselJ[n, z]) Failure Failure
Failed [57 / 63]
57/63]: [[-.7553141392+1.723217630*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}
.3969469092-.2695422112*I <- {z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = (- 1)^(m*n - 1)*((m - 1)*HankelH1(n, z)+ m*HankelH2(n, z)) HankelH1[n, z*Exp[m*Pi*I]] == (- 1)^(m*n - 1)*((m - 1)*HankelH1[n, z]+ m*HankelH2[n, z]) Failure Failure
Failed [57 / 63]
57/63]: [[-1.723217630-.7553141394*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}
.2695422111+.3969469092*I <- {z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = (- 1)^(m*n)*(m*HankelH1(n, z)+(m + 1)*HankelH2(n, z)) HankelH2[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)*(m*HankelH1[n, z]+(m + 1)*HankelH2[n, z]) Failure Failure
Failed [57 / 63]
57/63]: [[1.723217630+.755314139*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}
-.269542211-.396946909*I <- {z = 1/2*3^(1/2)+1/2*I, 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(z*sin(theta)) = BesselJ(0, z)+ 2*sum(BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity) Cos[z*Sin[\[Theta]]] == BesselJ[0, z]+ 2*Sum[BesselJ[2*k, z]*Cos[2*k*\[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(z*sin(theta)) = 2*sum(BesselJ(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity) Sin[z*Sin[\[Theta]]] == 2*Sum[BesselJ[2*k + 1, z]*Sin[(2*k + 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(z*cos(theta)) = BesselJ(0, z)+ 2*sum((- 1)^(k)* BesselJ(2*k, z)*cos(2*k*theta), k = 1..infinity) Cos[z*Cos[\[Theta]]] == BesselJ[0, z]+ 2*Sum[(- 1)^(k)* BesselJ[2*k, z]*Cos[2*k*\[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(z*cos(theta)) = 2*sum((- 1)^(k)* BesselJ(2*k + 1, z)*cos((2*k + 1)* theta), k = 0..infinity) Sin[z*Cos[\[Theta]]] == 2*Sum[(- 1)^(k)* BesselJ[2*k + 1, z]*Cos[(2*k + 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)+ 2*BesselJ(2, z)+ 2*BesselJ(4, z)+ 2*BesselJ(6, z)+ .. 1 == BesselJ[0, z]+ 2*BesselJ[2, z]+ 2*BesselJ[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)- 2*BesselJ(2, z)+ 2*BesselJ(4, z)- 2*BesselJ(6, z)+ .. Cos[z] == BesselJ[0, z]- 2*BesselJ[2, z]+ 2*BesselJ[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) = 2*BesselJ(1, z)- 2*BesselJ(3, z)+ 2*BesselJ(5, z)- .. Sin[z] == 2*BesselJ[1, z]- 2*BesselJ[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)*z*cos(z) = BesselJ(1, z)- 9*BesselJ(3, z)+ 25*BesselJ(5, z)- 49*BesselJ(7, z)+ .. Divide[1,2]*z*Cos[z] == BesselJ[1, z]- 9*BesselJ[3, z]+ 25*BesselJ[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)*z*sin(z) = 4*BesselJ(2, z)- 16*BesselJ(4, z)+ 36*BesselJ(6, z)- .. Divide[1,2]*z*Sin[z] == 4*BesselJ[2, z]- 16*BesselJ[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)^(2*n) = (- 1)^(n)* (lambda)^(2*n)* (z)^(- n)* w (w)^(2*n) == (- 1)^(n)* \[Lambda]^(2*n)* (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, nu*x)) <= ((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, nu*x), nu*x$(1) )) <= ((1 + (x)^(2))^((1)/(4)))/(x*(2*Pi*nu)^((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*(2*Pi*\[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, nu*x))/((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, nu*x))/((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, n*z)) <= (abs((z)^(n)* exp(n*(1 - (z)^(2))^((1)/(2)))))/((abs(1 +(1 - (z)^(2))^((1)/(2))))^(n)) Abs[BesselJ[n, n*z]] <= 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(nu*Pi)*(diff(BesselJ(nu, z), nu)- Pi*BesselY(nu, z))- csc(nu*Pi)*diff(BesselJ(- nu, z), nu)- Pi*BesselJ(nu, z) D[BesselY[\[Nu], z], \[Nu]] == Cot[\[Nu]*Pi]*(D[BesselJ[\[Nu], z], \[Nu]]- Pi*BesselY[\[Nu], z])- Csc[\[Nu]*Pi]*D[BesselJ[- \[Nu], z], \[Nu]]- Pi*BesselJ[\[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)/(Pi*z))^((1)/(2))* sin(z) BesselY[-Divide[1,2], z] == (Divide[2,Pi*z])^(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)/(Pi*z))^((1)/(2))* cos(z) - BesselY[Divide[1,2], z] == (Divide[2,Pi*z])^(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}} - I*HankelH1(-(1)/(2), z) = - I*((2)/(Pi*z))^((1)/(2))* exp(I*z) - I*HankelH1[-Divide[1,2], z] == - I*(Divide[2,Pi*z])^(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}} I*HankelH2(-(1)/(2), z) = I*((2)/(Pi*z))^((1)/(2))* exp(- I*z) I*HankelH2[-Divide[1,2], z] == I*(Divide[2,Pi*z])^(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[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]]] )) 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[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]]] )) 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[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]))) 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[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]))) 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(- I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, + 2*I*z) 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] Failure Successful
Failed [7 / 56]
7/56]: [[-.827986137e-1+.7317301038*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}
-.8060140108+.3257248263*I <- {nu = -1/2, z = -1/2+1/2*I*3^(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(+ I*z))/(GAMMA(nu + 1))*KummerM(nu +(1)/(2), 2*nu + 1, - 2*I*z) 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] Failure Successful
Failed [7 / 56]
7/56]: [[.827986132e-1-.7317301035*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}
.8060140102-.3257248264*I <- {nu = -1/2, z = -1/2+1/2*I*3^(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(-(2*nu + 1)* Pi*I/ 4))/((2)^(2*nu)* GAMMA(nu + 1))*(2*z)^(-(1)/(2))* WhittakerM(0, nu, + 2*I*z) BesselJ[\[Nu], z] == Divide[Exp[-(2*\[Nu]+ 1)* Pi*I/ 4],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]]*(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], + 2*I*z] Failure Failure
Failed [1 / 7]
1/7]: [[1.448710179-.1398527410*I <- {z = -1/2+1/2*I*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(+(2*nu + 1)* Pi*I/ 4))/((2)^(2*nu)* GAMMA(nu + 1))*(2*z)^(-(1)/(2))* WhittakerM(0, nu, - 2*I*z) BesselJ[\[Nu], z] == Divide[Exp[+(2*\[Nu]+ 1)* Pi*I/ 4],(2)^(2*\[Nu])* Gamma[\[Nu]+ 1]]*(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], - 2*I*z] Failure Failure
Failed [1 / 7]
1/7]: [[1.191860674-.595668984e-1*I <- {z = -1/2*3^(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)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z) = (exp(z))/(2*Pi)*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)* 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)) 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)* 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)) 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}]+ 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)] 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+.4999999994*I <- {z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}
.4999999994-.8660254030*I <- {z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(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+.4714045210*I <- {z = 3/2, zeta = 1/2*3^(1/2)+1/2*I}
-.2769653183-.6666666667*I <- {z = 3/2, zeta = -1/2+1/2*I*3^(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 - I*Pi)^((2)/(3)) \[Zeta] == (Divide[3,2])^(Divide[2,3])*(\[Tau]- I*Pi)^(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(- I*Pi/ 3)*tau \[Zeta] == Exp[- I*Pi/ 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 = +(tau*coth(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]: [[.8660254040-1.214547924*I <- {tau = 3/2, z = 1/2*3^(1/2)+1/2*I}
-.5000000000-.8485225201*I <- {tau = 3/2, z = -1/2+1/2*I*3^(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 = -(tau*coth(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+2.214547924*I <- {tau = 3/2, z = 1/2*3^(1/2)+1/2*I}
-.5000000000+2.580573328*I <- {tau = 3/2, z = -1/2+1/2*I*3^(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)(4*rho(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) = 2*c*int(BesselK(0, 2*c*sinh(t))*exp(- 2*nu*t), t = 0..infinity) D[c, \[Nu]] == 2*c*Integrate[BesselK[0, 2*c*Sinh[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)+ 46*mu - 63)*((lambda)^(3)- 1))/(6*(4*lambda)^(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)- 2053*mu + 1899)*((lambda)^(5)- 1))/(5*(4*lambda)^(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))/(8*lambda*(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)+ 46*mu - 63)* (lambda)^(3)-(mu - 1)*(mu - 25))/(6*(4*lambda)^(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)- 2053*mu + 1899)* (lambda)^(5)-(mu - 1)*((mu)^(2)- 114*mu + 1073))/(5*(4*lambda)^(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) = 2*sum(BesselJ(nu + 2*k + 1, x), k = 0..infinity) Integrate[BesselJ[\[Nu], t], {t, 0, x}, GenerateConditions->None] == 2*Sum[BesselJ[\[Nu]+ 2*k + 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(2*n, t), t = 0..x) = int(BesselJ(0, t), t = 0..x)- 2*sum(BesselJ(2*k + 1, x), k = 0..n - 1), int(BesselJ(2*n + 1, t), t = 0..x) Integrate[BesselJ[2*n, t], {t, 0, x}, GenerateConditions->None] == Integrate[BesselJ[0, t], {t, 0, x}, GenerateConditions->None]- 2*Sum[BesselJ[2*k + 1, x], {k, 0, n - 1}, GenerateConditions->None], Integrate[BesselJ[2*n + 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)- 2*sum(BesselJ(2*k + 1, x), k = 0..n - 1), int(BesselJ(2*n + 1, t), t = 0..x) = 1 - BesselJ(0, x)- 2*sum(BesselJ(2*k, x), k = 1..n) Integrate[BesselJ[0, t], {t, 0, x}, GenerateConditions->None]- 2*Sum[BesselJ[2*k + 1, x], {k, 0, n - 1}, GenerateConditions->None], Integrate[BesselJ[2*n + 1, t], {t, 0, x}, GenerateConditions->None] == 1 - BesselJ[0, x]- 2*Sum[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 + 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) 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] 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}} 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) 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] 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}} 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) 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] 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(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) 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] 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(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) 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] 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(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) 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] 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, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*(BesselJ(n, z))^(2) 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) 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(2*nu, 2*z*cos(theta))*cos(2*mu*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*cot(2*nu*Pi)*BesselJ(nu + mu, z)*BesselJ(nu - mu, z)-(1)/(2)*Pi*csc(2*nu*Pi)*BesselJ(mu - nu, z)*BesselJ(- mu - nu, z) Integrate[BesselY[2*\[Nu], 2*z*Cos[\[Theta]]]*Cos[2*\[Mu]*\[Theta]], {\[Theta], 0, Divide[1,2]*Pi}, GenerateConditions->None] == Divide[1,2]*Pi*Cot[2*\[Nu]*Pi]*BesselJ[\[Nu]+ \[Mu], z]*BesselJ[\[Nu]- \[Mu], z]-Divide[1,2]*Pi*Csc[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, 2*z*sin(theta))*cos(2*n*theta), theta = 0..(1)/(2)*Pi) = (1)/(2)*Pi*BesselJ(n, z)*BesselY(n, z) 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] 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, 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) 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] 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, 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) 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) 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, 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) 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] 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))^(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)) 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]] 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))^(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) 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, 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) 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] 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, 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))) 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))] 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) = 2*sum((nu + 2*k)* (BesselJ(nu + 2*k, x))^(2), k = 0..infinity) 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] 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) = 2*nu*(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) = 2*sum((- 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] == 2*Sum[(- 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))/(mu*nu*x) 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 + 2*k, 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]+ 2*k, 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(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] 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] 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(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] 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] 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)^(2*k))/(2*k*(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)^(2*k),2*k*((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)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(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[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((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)*nu*Pi) 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) = -(Pi*sec((1)/(2)*mu*Pi))/((2)^(mu)* (GAMMA((1)/(2)*mu +(1)/(2)))^(2)) 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)] 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, 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) 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] 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, a*t))/((t)^(2)+ (b)^(2)), t = 0..infinity) = - (b)^(nu - 1)* BesselK(nu, a*b) Integrate[Divide[(t)^\[Nu]* BesselY[\[Nu], a*t],(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, 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) 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] 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(- 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) 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)]] 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(- 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) 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)]] 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, 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))) 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)]] 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, 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))) 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)]] 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(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)) 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]) 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, 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) 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)]] 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 + 2*ell + 1, t)*BesselJ(nu + 2*m + 1, t), t = 0..infinity) = (KroneckerDelta[ell, m])/(2*(2*ell + nu + 1)) 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)] 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, 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) 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)]] 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, 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))) 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]]] 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, 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) 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)]] 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(- 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)) 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]] 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(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))) 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)]] 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(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))) 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)]] 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, 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) 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] 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, 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)) 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]]] 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, 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)) 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]]] 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(2*n - k, z), k = 0..2*n)+ 2*sum(BesselJ(k, z)*BesselJ(2*n + k, z), k = 1..infinity) = 0 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 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)+ 2*sum((- 1)^(k)* BesselJ(k, z)*BesselJ(n + k, z), k = 1..infinity) = BesselJ(n, 2*z) 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] 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)- 2*u*v*cos(alpha)) w == Sqrt[(u)^(2)+ (v)^(2)- 2*u*v*Cos[\[Alpha]]] Failure Failure
Failed [300 / 300]
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}
-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)}
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 - v*cos(alpha) = w*cos(chi) u - v*Cos[\[Alpha]] == w*Cos[\[Chi]] Failure Failure
Failed [300 / 300]
300/300]: [[-.263783978e-1+.4431282844*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, 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}
.8262683052-.3665121890*I <- {alpha = 3/2, chi = 1/2*3^(1/2)+1/2*I, 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)}
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}} v*sin(alpha) = w*sin(chi) v*Sin[\[Alpha]] == w*Sin[\[Chi]] Failure Failure
Failed [300 / 300]
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}
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)}
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(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) 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] 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 + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselJ(nu + 2*k, z), k = 0..infinity) (Divide[1,2]*z)^\[Nu] == Sum[Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselJ[\[Nu]+ 2*k, 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 + 2*k)* BesselJ(n + 2*k, 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 + 2*k)* BesselJ[n + 2*k, 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)])+ x*diff(w, x)+((x)^(2)+ (nu)^(2))* w = 0 (x)^(2)* D[w, {x, 2}]+ x*D[w, x]+((x)^(2)+ \[Nu]^(2))* w == 0 Failure Failure
Failed [300 / 300]
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}
.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}
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)*Pi*nu)*Re(BesselJ(I*nu, 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)*Pi*nu)*Re(BesselY(I*nu, 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 + I*nu) = ((Pi*nu)/(sinh(Pi*nu)))^((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-.6479738907*I <- {gamma = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, gamma[nu] = 1/2*3^(1/2)+1/2*I}
.2393622021-.2867640040*I <- {gamma = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, gamma[nu] = -1/2+1/2*I*3^(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-.1547836875*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}
-1.059084556+.9282601935*I <- {nu = 1/2*3^(1/2)+1/2*I, 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+.5898680353*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}
-.1980888923+.1736197856*I <- {nu = 1/2*3^(1/2)+1/2*I, 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-.7786157192*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}
-.6431025084-4.765445687*I <- {nu = 1/2*3^(1/2)+1/2*I, 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)])+ z*diff(w, z)-((z)^(2)+ (nu)^(2))* w = 0 (z)^(2)* D[w, {z, 2}]+ z*D[w, z]-((z)^(2)+ \[Nu]^(2))* w == 0 Failure Failure
Failed [220 / 300]
220/300]: [[-.6467477718e-9-2.000000002*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
-.8660254040e-9-2.000000001*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}
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(nu*Pi)*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]*Pi*Divide[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(- nu*Pi*I/ 2)*BesselJ(nu, z*exp(+ Pi*I/ 2)) BesselI[\[Nu], z] == Exp[- \[Nu]*Pi*I/ 2]*BesselJ[\[Nu], z*Exp[+ 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(+ nu*Pi*I/ 2)*BesselJ(nu, z*exp(- Pi*I/ 2)) BesselI[\[Nu], z] == Exp[+ \[Nu]*Pi*I/ 2]*BesselJ[\[Nu], z*Exp[- 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(- nu*Pi*I/ 2)*(HankelH1(nu, z*exp(+ Pi*I/ 2))+ HankelH2(nu, z*exp(+ Pi*I/ 2))) BesselI[\[Nu], z] == Divide[1,2]*Exp[- \[Nu]*Pi*I/ 2]*(HankelH1[\[Nu], z*Exp[+ Pi*I/ 2]]+ HankelH2[\[Nu], z*Exp[+ 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(+ nu*Pi*I/ 2)*(HankelH1(nu, z*exp(- Pi*I/ 2))+ HankelH2(nu, z*exp(- Pi*I/ 2))) BesselI[\[Nu], z] == Divide[1,2]*Exp[+ \[Nu]*Pi*I/ 2]*(HankelH1[\[Nu], z*Exp[- Pi*I/ 2]]+ HankelH2[\[Nu], z*Exp[- Pi*I/ 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}}} Pi*I*BesselJ(nu, z) = exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2))- exp(nu*Pi*I/ 2)*BesselK(nu, z*exp(Pi*I/ 2)) Pi*I*BesselJ[\[Nu], z] == Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]]- Exp[\[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[Pi*I/ 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}}} - Pi*BesselY(nu, z) = exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2))+ exp(nu*Pi*I/ 2)*BesselK(nu, z*exp(Pi*I/ 2)) - Pi*BesselY[\[Nu], z] == Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- Pi*I/ 2]]+ Exp[\[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[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)* Pi*I/ 2)*BesselI(nu, z*exp(- Pi*I/ 2))-(2/ Pi)* exp(- nu*Pi*I/ 2)*BesselK(nu, z*exp(- Pi*I/ 2)) BesselY[\[Nu], z] == Exp[+(\[Nu]+ 1)* Pi*I/ 2]*BesselI[\[Nu], z*Exp[- Pi*I/ 2]]-(2/ Pi)* Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[- 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)* Pi*I/ 2)*BesselI(nu, z*exp(+ Pi*I/ 2))-(2/ Pi)* exp(+ nu*Pi*I/ 2)*BesselK(nu, z*exp(+ Pi*I/ 2)) BesselY[\[Nu], z] == Exp[-(\[Nu]+ 1)* Pi*I/ 2]*BesselI[\[Nu], z*Exp[+ Pi*I/ 2]]-(2/ Pi)* Exp[+ \[Nu]*Pi*I/ 2]*BesselK[\[Nu], z*Exp[+ 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) = - 2*sin(nu*Pi)/(Pi*z) BesselI[\[Nu], z]*BesselI[- \[Nu]- 1, z]- BesselI[\[Nu]+ 1, z]*BesselI[- \[Nu], z] == - 2*Sin[\[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(+ z*cos(theta)), theta = 0..Pi) BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[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(- z*cos(theta)), theta = 0..Pi) BesselI[0, z] == Divide[1,Pi]*Integrate[Exp[- z*Cos[\[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(+ z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi) 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] 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(- z*cos(theta)), theta = 0..Pi) = (1)/(Pi)*int(cosh(z*cos(theta)), theta = 0..Pi) 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] 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(+ z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) 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] 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(- z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) 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] 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(+ 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) 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] 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(- 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) 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] 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(z*cos(theta))*cos(n*theta), theta = 0..Pi) BesselI[n, z] == Divide[1,Pi]*Integrate[Exp[z*Cos[\[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(z*cos(theta))*cos(nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*cosh(t)- nu*t), t = 0..infinity) 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] 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(+ z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi) BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[+ z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(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(- z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..Pi) BesselK[0, z] == -Divide[1,Pi]*Integrate[Exp[- z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(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(x*sinh(t)), t = 0..infinity) = int((cos(x*t))/(sqrt((t)^(2)+ 1)), t = 0..infinity) Integrate[Cos[x*Sinh[t]], {t, 0, Infinity}, GenerateConditions->None] == Integrate[Divide[Cos[x*t],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)*nu*Pi)*int(cos(x*sinh(t))*cosh(nu*t), t = 0..infinity) BesselK[\[Nu], x] == Sec[Divide[1,2]*\[Nu]*Pi]*Integrate[Cos[x*Sinh[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)*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) 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] 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(- z*cosh(t))*(sinh(t))^(2*nu), t = 0..infinity) 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] 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(- 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) 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] 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(- z*cosh(t))*cosh(nu*t), t = 0..infinity) BesselK[\[Nu], z] == Integrate[Exp[- z*Cosh[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))/(4*t))*(1)/((t)^(nu + 1)), t = 0..infinity) 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] 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 + 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) 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] 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)/(2*Pi*I)*int(exp(z*cosh(t)- nu*t), t = infinity - I*Pi..infinity + I*Pi) BesselI[\[Nu], z] == Divide[1,2*Pi*I]*Integrate[Exp[z*Cosh[t]- \[Nu]*t], {t, Infinity - I*Pi, 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))/(4*Pi*I)*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*z)^(- 2*t), t = c - I*infinity..c + I*infinity) 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] Failure Aborted
Failed [300 / 300]
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}
-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)}
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)/(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) 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] 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, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..(1)/(2)*Pi) 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] 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, 2*x*sinh(t))*exp((- mu + nu)* t), t = 0..infinity) BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]+ \[Nu], 2*x*Sinh[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, 2*x*sinh(t))*exp((- mu - nu)* t), t = 0..infinity) BesselI[\[Mu], x]*BesselK[\[Nu], x] == Integrate[BesselJ[\[Mu]- \[Nu], 2*x*Sinh[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) = 2*int(BesselK(mu + nu, 2*z*cosh(t))*cosh((mu - nu)* t), t = 0..infinity) BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]+ \[Nu], 2*z*Cosh[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) = 2*int(BesselK(mu - nu, 2*z*cosh(t))*cosh((mu + nu)* t), t = 0..infinity) BesselK[\[Mu], z]*BesselK[\[Nu], z] == 2*Integrate[BesselK[\[Mu]- \[Nu], 2*z*Cosh[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))/(2*t))*BesselK(nu, ((z*zeta)/(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),2*t]]*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)/(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) 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] Error Aborted - Skip - No test values generated