Results of Bessel Functions II: Difference between revisions

Revision as of 19:52, 15 October 2020

This is the second half of the chapter Bessel Functions. It shows the sections 10.33 to 10.73. For sections 10.2 to 10.32 go to Bessel Functions I.

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.34.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\modBesselI{\nu}@{z}}	`BesselI(nu, zexp(mPiI)) = exp(mnuPiI)*BesselI(nu, z)`	`BesselI[\[Nu], zExp[mPiI]] == Exp[m\[Nu]PiI]*BesselI[\[Nu], z]`	Failure	Failure	Failed [132 / 210] `132/210]: [[-2.206479866-1.131319388I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `.5147384726+.2724622562e-1I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [120 / 210] `{Complex[-2.206479866313521, -1.1313193889480602] <- {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[0.5147384728800724, 0.02724622519878004] <- {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]]]}`
10.34.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\modBesselK{\nu}@{z}-\pi i\sin@{m\nu\pi}\csc@{\nu\pi}\modBesselI{\nu}@{z}}	`BesselK(nu, zexp(mPiI)) = exp(- mnuPiI)BesselK(nu, z)- PiIsin(mnuPi)csc(nuPi)BesselI(nu, z)`	`BesselK[\[Nu], zExp[mPiI]] == Exp[- m\[Nu]PiI]BesselK[\[Nu], z]- PiISin[m\[Nu]Pi]Csc[\[Nu]Pi]BesselI[\[Nu], z]`	Failure	Failure	Failed [170 / 210] `170/210]: [[2.965939338+3.157233720I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `-10.37113928-12.75980866I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [162 / 210] `{Complex[2.965939340334436, 3.157233721966529] <- {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[-10.371139260352992, -12.75980869099896] <- {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]]]}`
10.34.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = (i/\pi)\left(+ e^{m\nu\pi i}\modBesselK{\nu}@{ze^{+\pi i}}- e^{(m- 1)\nu\pi i}\modBesselK{\nu}@{z}\right)}	`BesselI(nu, zexp(mPiI)) = (I/ Pi)(+ exp(mnuPiI)BesselK(nu, zexp(+ PiI))- exp((m - 1)* nuPiI)*BesselK(nu, z))`	`BesselI[\[Nu], zExp[mPiI]] == (I/ Pi)(+ Exp[m\[Nu]PiI]BesselK[\[Nu], zExp[+ PiI]]- Exp[(m - 1)* \[Nu]PiI]*BesselK[\[Nu], z])`	Failure	Failure	Failed [152 / 210] `152/210]: [[-2.316975457-.8668337446I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `.5132395470-.3232131754e-1I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [140 / 210] `{Complex[-2.3169754573845194, -0.8668337451474188] <- {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[0.5132395471581521, -0.03232131806579792] <- {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]]]}`
10.34.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{ze^{m\pi i}} = (i/\pi)\left(- e^{m\nu\pi i}\modBesselK{\nu}@{ze^{-\pi i}}+ e^{(m+ 1)\nu\pi i}\modBesselK{\nu}@{z}\right)}	`BesselI(nu, zexp(mPiI)) = (I/ Pi)(- exp(mnuPiI)BesselK(nu, zexp(- PiI))+ exp((m + 1)* nuPiI)*BesselK(nu, z))`	`BesselI[\[Nu], zExp[mPiI]] == (I/ Pi)(- Exp[m\[Nu]PiI]BesselK[\[Nu], zExp[- PiI]]+ Exp[(m + 1)* \[Nu]PiI]*BesselK[\[Nu], z])`	Failure	Failure	Failed [190 / 210] `190/210]: [[-2.206479866-1.131319388I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `.5147384726+.2724622561e-1I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [190 / 210] `{Complex[-2.206479866313521, -1.1313193889480602] <- {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[0.5147384728800724, 0.027246225198780036] <- {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]]]}`
10.34.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = \csc@{\nu\pi}\left(+\sin@{m\nu\pi}\modBesselK{\nu}@{ze^{+\pi i}}-\sin@{(m- 1)\nu\pi}\modBesselK{\nu}@{z}\right)}	`BesselK(nu, zexp(mPiI)) = csc(nuPi)(+ sin(mnuPi)BesselK(nu, zexp(+ PiI))- sin((m - 1)* nuPi)BesselK(nu, z))`	`BesselK[\[Nu], zExp[mPiI]] == Csc[\[Nu]Pi](+ Sin[m\[Nu]Pi]BesselK[\[Nu], zExp[+ PiI]]- Sin[(m - 1)* \[Nu]Pi]BesselK[\[Nu], z])`	Failure	Failure	Failed [158 / 210] `158/210]: [[-2.723238516+7.278993081I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}` `29.12762958-25.06220737I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 3}`	Failed [154 / 210] `{Complex[-2.7232385256388585, 7.278993075467058] <- {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]]]}` `Complex[29.127629620508102, -25.062207299552764] <- {Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.34.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{ze^{m\pi i}} = \csc@{\nu\pi}\left(-\sin@{m\nu\pi}\modBesselK{\nu}@{ze^{-\pi i}}+\sin@{(m+ 1)\nu\pi}\modBesselK{\nu}@{z}\right)}	`BesselK(nu, zexp(mPiI)) = csc(nuPi)(- sin(mnuPi)BesselK(nu, zexp(- PiI))+ sin((m + 1)* nuPi)BesselK(nu, z))`	`BesselK[\[Nu], zExp[mPiI]] == Csc[\[Nu]Pi](- Sin[m\[Nu]Pi]BesselK[\[Nu], zExp[- PiI]]+ Sin[(m + 1)* \[Nu]Pi]BesselK[\[Nu], z])`	Failure	Failure	Failed [170 / 210] `170/210]: [[2.965939338+3.157233717I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 1}` `-10.37113929-12.75980866I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, m = 2}`	Failed [182 / 210] `{Complex[2.9659393403344363, 3.1572337219665294] <- {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[-10.371139260352981, -12.759808690998973] <- {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]]]}`
10.34.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = (-1)^{mn}\modBesselK{n}@{z}+(-1)^{n(m-1)-1}m\pi i\modBesselI{n}@{z}}	`BesselK(n, zexp(mPiI)) = (- 1)^(mn)* BesselK(n, z)+(- 1)^(n(m - 1)- 1) mPiI*BesselI(n, z)`	`BesselK[n, zExp[mPiI]] == (- 1)^(mn)* BesselK[n, z]+(- 1)^(n(m - 1)- 1) mPiI*BesselI[n, z]`	Failure	Failure	Failed [57 / 63] `57/63]: [[-1.971501919+2.706233555I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 1}` `-.7368261646+.3579119854I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 2}`	Failed [48 / 63] `{Complex[-1.9715019183470535, 2.7062335550125516] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.736826162742255, 0.3579119863626685] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.34.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = +(-1)^{n(m-1)}m\modBesselK{n}@{ze^{+\pi i}}-(-1)^{nm}(m- 1)\modBesselK{n}@{z}}	`BesselK(n, zexp(mPiI)) = +(- 1)^(n(m - 1))* mBesselK(n, zexp(+ PiI))-(- 1)^(nm)(m - 1) BesselK(n, z)`	`BesselK[n, zExp[mPiI]] == +(- 1)^(n(m - 1))* mBesselK[n, zExp[+ PiI]]-(- 1)^(nm)(m - 1) BesselK[n, z]`	Failure	Failure	Failed [51 / 63] `51/63]: [[-1.971501920+2.706233556I <- {z = 1/23^(1/2)+1/2I, m = 2, n = 1}` `.7368261602-.357911988I <- {z = 1/23^(1/2)+1/2I, m = 2, n = 2}`	Failed [42 / 63] `{Complex[-1.9715019183470535, 2.7062335550125516] <- {Rule[m, 2], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.736826162742255, -0.3579119863626685] <- {Rule[m, 2], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.34.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{ze^{m\pi i}} = -(-1)^{n(m-1)}m\modBesselK{n}@{ze^{-\pi i}}+(-1)^{nm}(m+ 1)\modBesselK{n}@{z}}	`BesselK(n, zexp(mPiI)) = -(- 1)^(n(m - 1))* mBesselK(n, zexp(- PiI))+(- 1)^(nm)(m + 1) BesselK(n, z)`	`BesselK[n, zExp[mPiI]] == -(- 1)^(n(m - 1))* mBesselK[n, zExp[- PiI]]+(- 1)^(nm)(m + 1) BesselK[n, z]`	Failure	Failure	Failed [54 / 63] `54/63]: [[-1.971501919+2.706233556I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 1}` `-.7368261645+.357911985I <- {z = 1/23^(1/2)+1/2I, m = 1, n = 2}`	Failed [63 / 63] `{Complex[-1.9715019183470535, 2.7062335550125516] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.736826162742255, 0.3579119863626685] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.34#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{\conj{z}} = \conj{\modBesselI{\nu}@{z}}}	`BesselI(nu, conjugate(z)) = conjugate(BesselI(nu, z))`	`BesselI[\[Nu], Conjugate[z]] == Conjugate[BesselI[\[Nu], z]]`	Failure	Failure	Skipped - Because timed out	Failed [28 / 70] `{Complex[-0.1457476573229447, -0.7449450592023206] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.100244133383339, 1.2347828003590728] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.34#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{\conj{z}} = \conj{\modBesselK{\nu}@{z}}}	`BesselK(nu, conjugate(z)) = conjugate(BesselK(nu, z))`	`BesselK[\[Nu], Conjugate[z]] == Conjugate[BesselK[\[Nu], z]]`	Failure	Failure	Failed [28 / 70] `28/70]: [[-.3322466664+.1347267497I <- {nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `.8978926857-1.555608423I <- {nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}`	Failed [28 / 70] `{Complex[-0.332246666369582, 0.13472674975137633] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.23222824698313052, -0.12812607679285354] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.35.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}\modBesselI{m}@{z}}	`exp((1)/(2)z(t + (t)^(- 1))) = sum((t)^(m)* BesselI(m, z), m = - infinity..infinity)`	`Exp[Divide[1,2]z(t + (t)^(- 1))] == Sum[(t)^(m)* BesselI[m, z], {m, - Infinity, Infinity}, GenerateConditions->None]`	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
10.35.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\cos@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\modBesselI{k}@{z}\cos@{k\theta}}	`exp(zcos(theta)) = BesselI(0, z)+ 2sum(BesselI(k, z)cos(ktheta), k = 1..infinity)`	`Exp[zCos[\[Theta]]] == BesselI[0, z]+ 2Sum[BesselI[k, z]Cos[k\[Theta]], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Successful	Skipped - Because timed out	Successful [Tested: 70]
10.35.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\sin@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=0}^{\infty}(-1)^{k}\modBesselI{2k+1}@{z}\sin@{(2k+1)\theta}+2\sum_{k=1}^{\infty}(-1)^{k}\modBesselI{2k}@{z}\cos@{2k\theta}}	`exp(zsin(theta)) = BesselI(0, z)+ 2sum((- 1)^(k)* BesselI(2k + 1, z)sin((2k + 1) theta), k = 0..infinity)+ 2sum((- 1)^(k) BesselI(2k, z)cos(2ktheta), k = 1..infinity)`	`Exp[zSin[\[Theta]]] == BesselI[0, z]+ 2Sum[(- 1)^(k)* BesselI[2k + 1, z]Sin[(2k + 1) \[Theta]], {k, 0, Infinity}, GenerateConditions->None]+ 2Sum[(- 1)^(k) BesselI[2k, z]Cos[2k\[Theta]], {k, 1, Infinity}, GenerateConditions->None]`	Aborted	Failure	Manual Skip!	Skipped - Because timed out
10.35.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 = \modBesselI{0}@{z}-2\modBesselI{2}@{z}+2\modBesselI{4}@{z}-2\modBesselI{6}@{z}+\dotsb}	`1 = BesselI(0, z)- 2BesselI(2, z)+ 2BesselI(4, z)- 2*BesselI(6, z)+ ..`	`1 == BesselI[0, z]- 2BesselI[2, z]+ 2BesselI[4, z]- 2*BesselI[6, z]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-9.440290591519046^-8, -1.7199789187696823^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-9.924736610669727^-8, -1.6360842739013975^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.35.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{+ z} = \modBesselI{0}@{z}+ 2\modBesselI{1}@{z}+2\modBesselI{2}@{z}+ 2\modBesselI{3}@{z}+\dotsb}	`exp(+ z) = BesselI(0, z)+ 2BesselI(1, z)+ 2BesselI(2, z)+ 2*BesselI(3, z)+ ..`	`Exp[+ z] == BesselI[0, z]+ 2BesselI[1, z]+ 2BesselI[2, z]+ 2*BesselI[3, z]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-0.003384051289485407, 0.00475177611436145], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.002576303532707505, 0.004074841322498801], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.35.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{- z} = \modBesselI{0}@{z}- 2\modBesselI{1}@{z}+2\modBesselI{2}@{z}- 2\modBesselI{3}@{z}+\dotsb}	`exp(- z) = BesselI(0, z)- 2BesselI(1, z)+ 2BesselI(2, z)- 2*BesselI(3, z)+ ..`	`Exp[- z] == BesselI[0, z]- 2BesselI[1, z]+ 2BesselI[2, z]- 2*BesselI[3, z]+ \[Ellipsis]`	Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-0.0024389937896763803, 0.0042567403420422645], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.0020316532349716754, 0.004934003265463338], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.37.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\modBesselK{\nu}@{z}\| < \|\modBesselK{\mu}@{z}\|}	`abs(BesselK(nu, z)) < abs(BesselK(mu, z))`	`Abs[BesselK[\[Nu], z]] < Abs[BesselK[\[Mu], z]]`	Failure	Failure	Failed [204 / 300] `204/300]: [[.6496143723 < .6496143723 <- {mu = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I}` `3.110500858 < 3.110500858 <- {mu = 1/23^(1/2)+1/2I, nu = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)}`	Failed [184 / 300] `{False <- {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]]]}` `False <- {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[-5, 6]], Pi]]]}`
10.38.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{+\nu}@{z}}{\nu} = +\modBesselI{+\nu}@{z}\ln@{\tfrac{1}{2}z}-(\tfrac{1}{2}z)^{+\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1+\nu}}{\EulerGamma@{k+1+\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!}}	`diff(BesselI(+ nu, z), nu) = + BesselI(+ nu, z)ln((1)/(2)z)-((1)/(2)z)^(+ nu) sum((Psi(k + 1 + nu))/(GAMMA(k + 1 + nu))(((1)/(4)(z)^(2))^(k))/(factorial(k)), k = 0..infinity)`	`D[BesselI[+ \[Nu], z], \[Nu]] == + BesselI[+ \[Nu], z]Log[Divide[1,2]z]-(Divide[1,2]z)^(+ \[Nu]) Sum[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]}`
10.38.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{-\nu}@{z}}{\nu} = -\modBesselI{-\nu}@{z}\ln@{\tfrac{1}{2}z}+(\tfrac{1}{2}z)^{-\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1-\nu}}{\EulerGamma@{k+1-\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!}}	`diff(BesselI(- nu, z), nu) = - BesselI(- nu, z)ln((1)/(2)z)+((1)/(2)z)^(- nu) sum((Psi(k + 1 - nu))/(GAMMA(k + 1 - nu))(((1)/(4)(z)^(2))^(k))/(factorial(k)), k = 0..infinity)`	`D[BesselI[- \[Nu], z], \[Nu]] == - BesselI[- \[Nu], z]Log[Divide[1,2]z]+(Divide[1,2]z)^(- \[Nu]) Sum[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]}`
10.38.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselK{\nu}@{z}}{\nu} = \tfrac{1}{2}\pi\csc@{\nu\pi}\*\left(\pderiv{\modBesselI{-\nu}@{z}}{\nu}-\pderiv{\modBesselI{\nu}@{z}}{\nu}\right)-\pi\cot@{\nu\pi}\modBesselK{\nu}@{z}}	`diff(BesselK(nu, z), nu) = (1)/(2)Picsc(nuPi)(diff(BesselI(- nu, z), nu)- diff(BesselI(nu, z), nu))- Picot(nuPi)*BesselK(nu, z)`	`D[BesselK[\[Nu], z], \[Nu]] == Divide[1,2]PiCsc[\[Nu]Pi](D[BesselI[- \[Nu], z], \[Nu]]- D[BesselI[\[Nu], z], \[Nu]])- PiCot[\[Nu]Pi]*BesselK[\[Nu], z]`	Successful	Failure	-	Successful [Tested: 7]
10.39#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\sinh@@{z}}	`BesselI((1)/(2), z) = ((2)/(Piz))^((1)/(2)) sinh(z)`	`BesselI[Divide[1,2], z] == (Divide[2,Piz])^(Divide[1,2]) Sinh[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.39#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\frac{1}{2}}@{z} = \left(\frac{2}{\pi z}\right)^{\frac{1}{2}}\cosh@@{z}}	`BesselI(-(1)/(2), z) = ((2)/(Piz))^((1)/(2)) cosh(z)`	`BesselI[-Divide[1,2], z] == (Divide[2,Piz])^(Divide[1,2]) Cosh[z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.39.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{1}{2}}@{z} = \modBesselK{-\frac{1}{2}}@{z}}	`BesselK((1)/(2), z) = BesselK(-(1)/(2), z)`	`BesselK[Divide[1,2], z] == BesselK[-Divide[1,2], z]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
10.39.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\frac{1}{2}}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}}	`BesselK(-(1)/(2), z) = ((Pi)/(2z))^((1)/(2)) exp(- z)`	`BesselK[-Divide[1,2], z] == (Divide[Pi,2z])^(Divide[1,2]) Exp[- z]`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.39.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{1}{4}}@{z} = \pi^{\frac{1}{2}}z^{-\frac{1}{4}}\paraU@{0}{2z^{\frac{1}{2}}}}	`BesselK((1)/(4), z) = (Pi)^((1)/(2))* (z)^(-(1)/(4))* CylinderU(0, 2*(z)^((1)/(2)))`	`BesselK[Divide[1,4], z] == (Pi)^(Divide[1,2])* (z)^(-Divide[1,4])* ParabolicCylinderD[- 1/2 -(0), 2*(z)^(Divide[1,2])]`	Successful	Failure	-	Successful [Tested: 7]
10.39.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\frac{3}{4}}@{z} = \tfrac{1}{2}\pi^{\frac{1}{2}}z^{-\frac{3}{4}}\left(\tfrac{1}{2}\paraU@{1}{2z^{\frac{1}{2}}}+\paraU@{-1}{2z^{\frac{1}{2}}}\right)}	`BesselK((3)/(4), z) = (1)/(2)(Pi)^((1)/(2)) (z)^(-(3)/(4))((1)/(2)CylinderU(1, 2(z)^((1)/(2)))+ CylinderU(- 1, 2(z)^((1)/(2))))`	`BesselK[Divide[3,4], z] == Divide[1,2](Pi)^(Divide[1,2]) (z)^(-Divide[3,4])(Divide[1,2]ParabolicCylinderD[- 1/2 -(1), 2(z)^(Divide[1,2])]+ ParabolicCylinderD[- 1/2 -(- 1), 2(z)^(Divide[1,2])])`	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
10.39.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{+ z}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{- 2z}}	`BesselI(nu, z) = (((1)/(2)z)^(nu) exp(+ z))/(GAMMA(nu + 1))KummerM(nu +(1)/(2), 2nu + 1, - 2*z)`	`BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu] Exp[+ z],Gamma[\[Nu]+ 1]]Hypergeometric1F1[\[Nu]+Divide[1,2], 2\[Nu]+ 1, - 2*z]`	Failure	Successful	Failed [7 / 56] `7/56]: [[-.800260207-.3396157390I <- {nu = -1/2, z = 1/23^(1/2)+1/2I}` `-.4588638571-.5759587792I <- {nu = -1/2, z = -1/2+1/2I3^(1/2)}`	Failed [7 / 56] `{Complex[-0.8002602062152042, -0.3396157389151986] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}` `Complex[-0.45886385712966904, -0.5759587792371148] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]}`
10.39.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(\tfrac{1}{2}z)^{\nu}e^{- z}}{\EulerGamma@{\nu+1}}\KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{+ 2z}}	`BesselI(nu, z) = (((1)/(2)z)^(nu) exp(- z))/(GAMMA(nu + 1))KummerM(nu +(1)/(2), 2nu + 1, + 2*z)`	`BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu] Exp[- z],Gamma[\[Nu]+ 1]]Hypergeometric1F1[\[Nu]+Divide[1,2], 2\[Nu]+ 1, + 2*z]`	Successful	Successful	Skip - symbolical successful subtest	Failed [7 / 56] `{Complex[0.8002602062152032, 0.3396157389151989] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -0.5]}` `Complex[0.4588638571296689, 0.575958779237115] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, -0.5]}`
10.39.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \pi^{\frac{1}{2}}(2z)^{\nu}e^{-z}\KummerconfhyperU@{\nu+\tfrac{1}{2}}{2\nu+1}{2z}}	`BesselK(nu, z) = (Pi)^((1)/(2))(2z)^(nu)* exp(- z)KummerU(nu +(1)/(2), 2nu + 1, 2*z)`	`BesselK[\[Nu], z] == (Pi)^(Divide[1,2])(2z)^\[Nu]* Exp[- z]HypergeometricU[\[Nu]+Divide[1,2], 2\[Nu]+ 1, 2*z]`	Successful	Successful	-	Successful [Tested: 70]
10.39.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \frac{(2z)^{-\frac{1}{2}}\WhittakerconfhyperM{0}{\nu}@{2z}}{2^{2\nu}\EulerGamma@{\nu+1}}}	`BesselI(nu, z) = ((2z)^(-(1)/(2)) WhittakerM(0, nu, 2z))/((2)^(2nu)* GAMMA(nu + 1))`	`BesselI[\[Nu], z] == Divide[(2z)^(-Divide[1,2]) WhittakerM[0, \[Nu], 2z],(2)^(2\[Nu])* Gamma[\[Nu]+ 1]]`	Successful	Successful	-	Successful [Tested: 7]
10.39.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}\WhittakerconfhyperW{0}{\nu}@{2z}}	`BesselK(nu, z) = ((Pi)/(2z))^((1)/(2)) WhittakerW(0, nu, 2*z)`	`BesselK[\[Nu], z] == (Divide[Pi,2z])^(Divide[1,2]) WhittakerW[0, \[Nu], 2*z]`	Failure	Failure	Successful [Tested: 70]	Successful [Tested: 70]
10.39.E9	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}}{\EulerGamma@{\nu+1}}\genhyperF{0}{1}@{-}{\nu+1}{\tfrac{1}{4}z^{2}}}	`BesselI(nu, z) = (((1)/(2)z)^(nu))/(GAMMA(nu + 1))hypergeom([-], [nu + 1], (1)/(4)*(z)^(2))`	`BesselI[\[Nu], z] == Divide[(Divide[1,2]z)^\[Nu],Gamma[\[Nu]+ 1]]HypergeometricPFQ[{-}, {\[Nu]+ 1}, Divide[1,4]*(z)^(2)]`	Error	Failure	-	Error
10.40.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right)}	`BesselK(nu, z) = ((Pi)/(2z))^((1)/(2)) exp(- z)(sum((a[k](nu))/((z)^(k)), k = 0..ell - 1)+ R[ell]*(nu , z))`	`BesselK[\[Nu], z] == (Divide[Pi,2z])^(Divide[1,2]) Exp[- z](Sum[Divide[Subscript[a, k](\[Nu]),(z)^(k)], {k, 0, \[ScriptL]- 1}, GenerateConditions->None]+ Subscript[R, \[ScriptL]]*(\[Nu], z))`	Failure	Failure	Error	Error
10.40.E13	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}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{2z}+R_{m,\ell}(\nu,z)\right)}	`R[ell](nu , z) = (- 1)^(ell) 2cos(nuPi)(sum((a[k](nu))/((z)^(k))(exp(2z)/(2Pi))GAMMA(ell - k)GAMMA(1-ell - k,2z), k = 0..m - 1)+ R[m , ell]*(nu , z))`	`Error`	Error	Missing Macro Error	-	-
10.41.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p = (1+z^{2})^{-\frac{1}{2}}}	`p = (1 + (z)^(2))^(-(1)/(2))`	`p == (1 + (z)^(2))^(-Divide[1,2])`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.41#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{1}(p) = \tfrac{1}{24}(3p-5p^{3})}	`U[1](p) = (1)/(24)(3p - 5(p)^(3))`	`Subscript[U, 1](p) == Divide[1,24](3p - 5(p)^(3))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.41#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{2}(p) = \tfrac{1}{1152}(81p^{2}-462p^{4}+385p^{6})}	`U[2](p) = (1)/(1152)(81(p)^(2)- 462(p)^(4)+ 385*(p)^(6))`	`Subscript[U, 2](p) == Divide[1,1152](81(p)^(2)- 462(p)^(4)+ 385*(p)^(6))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.41#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{3}(p) = \tfrac{1}{4\;14720}\*(30375p^{3}-3\;69603p^{5}+7\;65765p^{7}-4\;25425p^{9})}	`U[3](p) = (1)/(414720)(30375(p)^(3)- 369603(p)^(5)+ 765765(p)^(7)- 425425(p)^(9))`	`Subscript[U, 3](p) == Divide[1,414720](30375(p)^(3)- 369603(p)^(5)+ 765765(p)^(7)- 425425(p)^(9))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.41#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{1}(p) = \tfrac{1}{24}(-9p+7p^{3})}	`V[1](p) = (1)/(24)(- 9p + 7(p)^(3))`	`Subscript[V, 1](p) == Divide[1,24](- 9p + 7(p)^(3))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.41#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{2}(p) = \tfrac{1}{1152}(-135p^{2}+594p^{4}-455p^{6})}	`V[2](p) = (1)/(1152)(- 135(p)^(2)+ 594(p)^(4)- 455*(p)^(6))`	`Subscript[V, 2](p) == Divide[1,1152](- 135(p)^(2)+ 594(p)^(4)- 455*(p)^(6))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.41#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V_{3}(p) = \tfrac{1}{4\;14720}\*(-42525p^{3}+4\;51737p^{5}-8\;83575p^{7}+4\;75475p^{9})}	`V[3](p) = (1)/(414720)(- 42525(p)^(3)+ 451737(p)^(5)- 883575(p)^(7)+ 475475(p)^(9))`	`Subscript[V, 3](p) == Divide[1,414720](- 42525(p)^(3)+ 451737(p)^(5)- 883575(p)^(7)+ 475475(p)^(9))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.43.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}\frac{\modBesselI{0}@{t}-1}{t}\diff{t} = \frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x}}	`int((BesselI(0, t)- 1)/(t), t = 0..x) = (1)/(2)sum((- 1)^(k - 1)(Psi(k + 1)- Psi(1))/(factorial(k))((1)/(2)x)^(k)* BesselI(k, x), k = 1..infinity)`	`Integrate[Divide[BesselI[0, t]- 1,t], {t, 0, x}, GenerateConditions->None] == Divide[1,2]Sum[(- 1)^(k - 1)Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!](Divide[1,2]x)^(k)* BesselI[k, x], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Failure	Successful [Tested: 3]	Failed [3 / 3] `{Plus[DirectedInfinity[-1], Times[-0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.75, k], BesselI[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[DirectedInfinity[-1], Times[-0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.25, k], BesselI[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]}`
10.43.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x} = \frac{2}{x}\sum_{k=0}^{\infty}(-1)^{k}(2k+3)(\digamma@{k+2}-\digamma@{1})\modBesselI{2k+3}@{x}}	`(1)/(2)sum((- 1)^(k - 1)(Psi(k + 1)- Psi(1))/(factorial(k))((1)/(2)x)^(k)* BesselI(k, x), k = 1..infinity) = (2)/(x)sum((- 1)^(k)(2k + 3)(Psi(k + 2)- Psi(1))* BesselI(2*k + 3, x), k = 0..infinity)`	`Divide[1,2]Sum[(- 1)^(k - 1)Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!](Divide[1,2]x)^(k)* BesselI[k, x], {k, 1, Infinity}, GenerateConditions->None] == Divide[2,x]Sum[(- 1)^(k)(2k + 3)(PolyGamma[k + 2]- PolyGamma[1])* BesselI[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Successful [Tested: 3]	Failed [3 / 3] `{Plus[Times[0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.75, k], BesselI[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.3333333333333333, NSum[Times[Power[-1, k], Plus[3, Times[2, k]], BesselI[Plus[3, Times[2, k]], 1.5], Plus[EulerGamma, PolyGamma[0, Plus[2, k]]]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}` `Plus[Times[0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.25, k], BesselI[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-4.0, NSum[Times[Power[-1, k], Plus[3, Times[2, k]], BesselI[Plus[3, Times[2, k]], 0.5], Plus[EulerGamma, PolyGamma[0, Plus[2, k]]]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}`
10.43.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}\frac{\modBesselK{0}@{t}}{t}\diff{t} = \frac{1}{2}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi^{2}}{24}-\sum_{k=1}^{\infty}\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}}	`int((BesselK(0, t))/(t), t = x..infinity) = (1)/(2)(ln((1)/(2)x)+ gamma)^(2)+((Pi)^(2))/(24)- sum((Psi(k + 1)+(1)/(2k)- ln((1)/(2)x))(((1)/(2)x)^(2k))/(2k*(factorial(k))^(2)), k = 1..infinity)`	`Integrate[Divide[BesselK[0, t],t], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2](Log[Divide[1,2]x]+ EulerGamma)^(2)+Divide[(Pi)^(2),24]- Sum[(PolyGamma[k + 1]+Divide[1,2k]- Log[Divide[1,2]x])Divide[(Divide[1,2]x)^(2k),2k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 3]	Skipped - Because timed out
10.43.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{-t}\modBesselI{n}@{t}\diff{t} = xe^{-x}(\modBesselI{0}@{x}+\modBesselI{1}@{x})+n(e^{-x}\modBesselI{0}@{x}-1)+2e^{-x}\sum_{k=1}^{n-1}(n-k)\modBesselI{k}@{x}}	`int(exp(- t)BesselI(n, t), t = 0..x) = xexp(- x)(BesselI(0, x)+ BesselI(1, x))+ n(exp(- x)BesselI(0, x)- 1)+ 2exp(- x)sum((n - k) BesselI(k, x), k = 1..n - 1)`	`Integrate[Exp[- t]BesselI[n, t], {t, 0, x}, GenerateConditions->None] == xExp[- x](BesselI[0, x]+ BesselI[1, x])+ n(Exp[- x]BesselI[0, x]- 1)+ 2Exp[- x]Sum[(n - k) BesselI[k, x], {k, 1, n - 1}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 3]	Failed [2 / 3] {Plus[1.0269197346695518, Times[-0.44626032029685964, Plus[-4.940169569318671, Times[3.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[1.5, []], Times[Plus[-2, Times[-2, ], Times[-1, 1.5]], [Plus[1, ]]], Times[Plus[2, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[1.5, [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], BesselI[0, 1.5]], Equal[[2], Plus[BesselI[0, 1.5], BesselI[1, 1.5]]]}]][3.0]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], 1.5, []], Times[-1, Plus[2, ], Plus[Times[2, ], 1.5], [Plus[1, ]]], Times[, Plus[4, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[, 1.5, [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], BesselI[1, 1.5]], Equal[[3], Plus[Times[2, Power[1.5, -1], Plus[Times[1.5, BesselI[0, 1.5]], Times[-2, BesselI[1, 1.5]]]], BesselI[1, 1.5]]]}]][3.0]]]]], {Rule[n, 3], Rule[x, 1.5]} `Plus[0.6643873281588137, Times[-1.2130613194252668, Plus[-3.19045011222397, Times[3.0, DifferenceRoot[Func`
10.43.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}-\modBesselI{\nu+1}@{x})}	`int(exp(+ t)(t)^(nu) BesselI(nu, t), t = 0..x) = (exp(+ x)(x)^(nu + 1))/(2nu + 1)*(BesselI(nu, x)- BesselI(nu + 1, x))`	`Integrate[Exp[+ t](t)^\[Nu] BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x](x)^(\[Nu]+ 1),2\[Nu]+ 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]+ 1, x])`	Failure	Successful	Successful [Tested: 15]	Successful [Tested: 15]
10.43.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}+\modBesselI{\nu+1}@{x})}	`int(exp(- t)(t)^(nu) BesselI(nu, t), t = 0..x) = (exp(- x)(x)^(nu + 1))/(2nu + 1)*(BesselI(nu, x)+ BesselI(nu + 1, x))`	`Integrate[Exp[- t](t)^\[Nu] BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x](x)^(\[Nu]+ 1),2\[Nu]+ 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]+ 1, x])`	Failure	Successful	Skipped - Because timed out	Successful [Tested: 15]
10.43.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{+ x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}-\modBesselI{\nu-1}@{x})-\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}}	`int(exp(+ t)(t)^(- nu) BesselI(nu, t), t = 0..x) = -(exp(+ x)(x)^(- nu + 1))/(2nu - 1)(BesselI(nu, x)- BesselI(nu - 1, x))-((2)^(- nu + 1))/((2nu - 1)* GAMMA(nu))`	`Integrate[Exp[+ t](t)^(- \[Nu]) BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[+ x](x)^(- \[Nu]+ 1),2\[Nu]- 1](BesselI[\[Nu], x]- BesselI[\[Nu]- 1, x])-Divide[(2)^(- \[Nu]+ 1),(2\[Nu]- 1)* Gamma[\[Nu]]]`	Failure	Successful	Manual Skip!	Failed [3 / 12] `{0.39894228040143315 <- {Rule[x, 1.5], Rule[ν, 1.5]}` `0.39894228040143254 <- {Rule[x, 0.5], Rule[ν, 1.5]}`
10.43.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{- x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}+\modBesselI{\nu-1}@{x})+\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}}	`int(exp(- t)(t)^(- nu) BesselI(nu, t), t = 0..x) = -(exp(- x)(x)^(- nu + 1))/(2nu - 1)(BesselI(nu, x)+ BesselI(nu - 1, x))+((2)^(- nu + 1))/((2nu - 1)* GAMMA(nu))`	`Integrate[Exp[- t](t)^(- \[Nu]) BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[- x](x)^(- \[Nu]+ 1),2\[Nu]- 1](BesselI[\[Nu], x]+ BesselI[\[Nu]- 1, x])+Divide[(2)^(- \[Nu]+ 1),(2\[Nu]- 1)* Gamma[\[Nu]]]`	Failure	Successful	Manual Skip!	Successful [Tested: 12]
10.43.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{+ t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}+\modBesselK{\nu+1}@{x})-\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}}	`int(exp(+ t)(t)^(nu) BesselK(nu, t), t = 0..x) = (exp(+ x)(x)^(nu + 1))/(2nu + 1)(BesselK(nu, x)+ BesselK(nu + 1, x))-((2)^(nu) GAMMA(nu + 1))/(2*nu + 1)`	`Integrate[Exp[+ t](t)^\[Nu] BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x](x)^(\[Nu]+ 1),2\[Nu]+ 1](BesselK[\[Nu], x]+ BesselK[\[Nu]+ 1, x])-Divide[(2)^\[Nu] Gamma[\[Nu]+ 1],2*\[Nu]+ 1]`	Failure	Aborted	Manual Skip!	Failed [9 / 15] `{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 1.5]}` `DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 0.5]}`
10.43.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{x}e^{- t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}-\modBesselK{\nu+1}@{x})+\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}}	`int(exp(- t)(t)^(nu) BesselK(nu, t), t = 0..x) = (exp(- x)(x)^(nu + 1))/(2nu + 1)(BesselK(nu, x)- BesselK(nu + 1, x))+((2)^(nu) GAMMA(nu + 1))/(2*nu + 1)`	`Integrate[Exp[- t](t)^\[Nu] BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x](x)^(\[Nu]+ 1),2\[Nu]+ 1](BesselK[\[Nu], x]- BesselK[\[Nu]+ 1, x])+Divide[(2)^\[Nu] Gamma[\[Nu]+ 1],2*\[Nu]+ 1]`	Failure	Successful	Manual Skip!	Failed [3 / 15] `{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 2]}` `DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]}`
10.43.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{x}^{\infty}e^{t}t^{-\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{x}x^{-\nu+1}}{2\nu-1}(\modBesselK{\nu}@{x}+\modBesselK{\nu-1}@{x})}	`int(exp(t)(t)^(- nu) BesselK(nu, t), t = x..infinity) = (exp(x)(x)^(- nu + 1))/(2nu - 1)*(BesselK(nu, x)+ BesselK(nu - 1, x))`	`Integrate[Exp[t](t)^(- \[Nu]) BesselK[\[Nu], t], {t, x, Infinity}, GenerateConditions->None] == Divide[Exp[x](x)^(- \[Nu]+ 1),2\[Nu]- 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]- 1, x])`	Failure	Successful	Manual Skip!	Failed [3 / 9] `{Indeterminate <- {Rule[x, 1.5], Rule[ν, 2]}` `DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]}`
10.43.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselK{\nu}@{t}\diff{t} = \tfrac{1}{2}\pi\sec@{\tfrac{1}{2}\pi\nu}}	`int(BesselK(nu, t), t = 0..infinity) = (1)/(2)Pisec((1)/(2)Pinu)`	`Integrate[BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]PiSec[Divide[1,2]Pi\[Nu]]`	Successful	Successful	-	Successful [Tested: 6]
10.43.E19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu-1}\modBesselK{\nu}@{t}\diff{t} = 2^{\mu-2}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu}}	`int((t)^(mu - 1)* BesselK(nu, t), t = 0..infinity) = (2)^(mu - 2)* GAMMA((1)/(2)mu -(1)/(2)nu)GAMMA((1)/(2)mu +(1)/(2)*nu)`	`Integrate[(t)^(\[Mu]- 1)* BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == (2)^(\[Mu]- 2)* Gamma[Divide[1,2]\[Mu]-Divide[1,2]\[Nu]]Gamma[Divide[1,2]\[Mu]+Divide[1,2]*\[Nu]]`	Successful	Successful	-	Successful [Tested: 18]
10.43.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{at}\modBesselK{0}@{t}\diff{t} = \frac{\pi}{2(1+a^{2})^{\frac{1}{2}}}}	`int(cos(at)BesselK(0, t), t = 0..infinity) = (Pi)/(2*(1 + (a)^(2))^((1)/(2)))`	`Integrate[Cos[at]BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2*(1 + (a)^(2))^(Divide[1,2])]`	Successful	Aborted	-	Successful [Tested: 6]
10.43.E21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\sin@{at}\modBesselK{0}@{t}\diff{t} = \frac{\asinh@@{a}}{(1+a^{2})^{\frac{1}{2}}}}	`int(sin(at)BesselK(0, t), t = 0..infinity) = (arcsinh(a))/((1 + (a)^(2))^((1)/(2)))`	`Integrate[Sin[at]BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[ArcSinh[a],(1 + (a)^(2))^(Divide[1,2])]`	Failure	Successful	Successful [Tested: 0]	Successful [Tested: 6]
10.43.E23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\nu+1}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp@{\frac{b^{2}}{4p^{2}}}}	`int((t)^(nu + 1)* BesselI(nu, bt)exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = ((b)^(nu))/((2(p)^(2))^(nu + 1))exp(((b)^(2))/(4*(p)^(2)))`	`Integrate[(t)^(\[Nu]+ 1)* BesselI[\[Nu], bt]Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[(b)^\[Nu],(2(p)^(2))^(\[Nu]+ 1)]Exp[Divide[(b)^(2),4*(p)^(2)]]`	Error	Aborted	-	Skip - No test values generated
10.43.E24	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselI{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}}	`int(BesselI(nu, bt)exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(2p)exp(((b)^(2))/(8(p)^(2)))BesselI((1)/(2)nu, ((b)^(2))/(8(p)^(2)))`	`Integrate[BesselI[\[Nu], bt]Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],2p]Exp[Divide[(b)^(2),8(p)^(2)]]BesselI[Divide[1,2]\[Nu], Divide[(b)^(2),8(p)^(2)]]`	Failure	Aborted	Failed [228 / 300] `228/300]: [[-.7585567167+3.675115279I <- {b = -3/2, nu = 1/23^(1/2)+1/2I, p = 1/23^(1/2)+1/2I}` `-.9489546609+2.381017603I <- {b = -3/2, nu = 1/23^(1/2)+1/2I, p = -1/23^(1/2)-1/2I}`	Failed [152 / 300] `{Complex[-0.19039794459564638, -1.294097675814569] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[2.992047945390181, -4.249025046528451] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.43.E25	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\modBesselK{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{4p}\sec@{\tfrac{1}{2}\pi\nu}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselK{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}}	`int(BesselK(nu, bt)exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(4p)sec((1)/(2)Pinu)exp(((b)^(2))/(8(p)^(2)))BesselK((1)/(2)nu, ((b)^(2))/(8*(p)^(2)))`	`Integrate[BesselK[\[Nu], bt]Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],4p]Sec[Divide[1,2]Pi\[Nu]]Exp[Divide[(b)^(2),8(p)^(2)]]BesselK[Divide[1,2]\[Nu], Divide[(b)^(2),8*(p)^(2)]]`	Failure	Aborted	Failed [144 / 288] `144/288]: [[-.4056916296-1.844454275I <- {b = -3/2, nu = 1/23^(1/2)+1/2I, p = 1/23^(1/2)+1/2I}` `-.2830456904e-1-1.996429597I <- {b = -3/2, nu = 1/23^(1/2)+1/2I, p = 3/2}`	Failed [144 / 288] `{Complex[0.40569163152223653, 1.8444542715605226] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.4232355421098407, -0.8203643961026106] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.43.E26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\frac{\modBesselK{\mu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{b^{\nu}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\lambda-\frac{1}{2}\mu+\frac{1}{2}}}{2^{\lambda+1}a^{\nu-\lambda+1}}\*\hyperOlverF@{\frac{\nu-\lambda+\mu+1}{2}}{\frac{\nu-\lambda-\mu+1}{2}}{\nu+1}{-\frac{b^{2}}{a^{2}}}}	`int((BesselK(mu, at)BesselJ(nu, bt))/((t)^(lambda)), t = 0..infinity) = ((b)^(nu) GAMMA((1)/(2)nu -(1)/(2)lambda +(1)/(2)mu +(1)/(2))GAMMA((1)/(2)nu -(1)/(2)lambda -(1)/(2)mu +(1)/(2)))/((2)^(lambda + 1) (a)^(nu - lambda + 1))* hypergeom([(nu - lambda + mu + 1)/(2), (nu - lambda - mu + 1)/(2)], [nu + 1], -((b)^(2))/((a)^(2)))/GAMMA(nu + 1)`	`Integrate[Divide[BesselK[\[Mu], at]BesselJ[\[Nu], bt],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(b)^\[Nu] Gamma[Divide[1,2]\[Nu]-Divide[1,2]\[Lambda]+Divide[1,2]\[Mu]+Divide[1,2]]Gamma[Divide[1,2]\[Nu]-Divide[1,2]\[Lambda]-Divide[1,2]\[Mu]+Divide[1,2]],(2)^(\[Lambda]+ 1) (a)^(\[Nu]- \[Lambda]+ 1)]* Hypergeometric2F1Regularized[Divide[\[Nu]- \[Lambda]+ \[Mu]+ 1,2], Divide[\[Nu]- \[Lambda]- \[Mu]+ 1,2], \[Nu]+ 1, -Divide[(b)^(2),(a)^(2)]]`	Error	Aborted	-	Skip - No test values generated
10.43.E27	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\mu+\nu+1}\modBesselK{\mu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \frac{(2a)^{\mu}(2b)^{\nu}\EulerGamma@{\mu+\nu+1}}{(a^{2}+b^{2})^{\mu+\nu+1}}}	`int((t)^(mu + nu + 1)* BesselK(mu, at)BesselJ(nu, bt), t = 0..infinity) = ((2a)^(mu)(2b)^(nu)* GAMMA(mu + nu + 1))/(((a)^(2)+ (b)^(2))^(mu + nu + 1))`	`Integrate[(t)^(\[Mu]+ \[Nu]+ 1)* BesselK[\[Mu], at]BesselJ[\[Nu], bt], {t, 0, Infinity}, GenerateConditions->None] == Divide[(2a)^\[Mu](2b)^\[Nu]* Gamma[\[Mu]+ \[Nu]+ 1],((a)^(2)+ (b)^(2))^(\[Mu]+ \[Nu]+ 1)]`	Error	Aborted	-	Skip - No test values generated
10.43.E28	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}}\modBesselI{\nu}@{at}\modBesselI{\nu}@{bt}\diff{t} = \frac{1}{2p^{2}}\exp@{\frac{a^{2}+b^{2}}{4p^{2}}}\modBesselI{\nu}@{\frac{ab}{2p^{2}}}}	`int(texp(- (p)^(2) (t)^(2))BesselI(nu, at)BesselI(nu, bt), t = 0..infinity) = (1)/(2(p)^(2))exp(((a)^(2)+ (b)^(2))/(4(p)^(2)))BesselI(nu, (ab)/(2(p)^(2)))`	`Integrate[tExp[- (p)^(2) (t)^(2)]BesselI[\[Nu], at]BesselI[\[Nu], bt], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2(p)^(2)]Exp[Divide[(a)^(2)+ (b)^(2),4(p)^(2)]]BesselI[\[Nu], Divide[ab,2(p)^(2)]]`	Error	Aborted	-	Skipped - Because timed out
10.43.E29	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}}\modBesselI{0}@{at}\modBesselK{0}@{at}\diff{t} = \frac{1}{4p^{2}}\exp@{\frac{a^{2}}{2p^{2}}}\modBesselK{0}@{\frac{a^{2}}{2p^{2}}}}	`int(texp(- (p)^(2) (t)^(2))BesselI(0, at)BesselK(0, at), t = 0..infinity) = (1)/(4(p)^(2))exp(((a)^(2))/(2(p)^(2)))BesselK(0, ((a)^(2))/(2*(p)^(2)))`	`Integrate[tExp[- (p)^(2) (t)^(2)]BesselI[0, at]BesselK[0, at], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,4(p)^(2)]Exp[Divide[(a)^(2),2(p)^(2)]]BesselK[0, Divide[(a)^(2),2*(p)^(2)]]`	Failure	Aborted	Skipped - Because timed out	Successful [Tested: 48]
10.44#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \sum_{k=0}^{\infty}\frac{z^{k}}{k!}\BesselJ{\nu+k}@{z}}	`BesselI(nu, z) = sum(((z)^(k))/(factorial(k))*BesselJ(nu + k, z), k = 0..infinity)`	`BesselI[\[Nu], z] == Sum[Divide[(z)^(k),(k)!]*BesselJ[\[Nu]+ k, z], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Successful	Skipped - Because timed out	Successful [Tested: 70]
10.44#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{z} = \sum_{k=0}^{\infty}(-1)^{k}\frac{z^{k}}{k!}\modBesselI{\nu+k}@{z}}	`BesselJ(nu, z) = sum((- 1)^(k)((z)^(k))/(factorial(k))BesselI(nu + k, z), k = 0..infinity)`	`BesselJ[\[Nu], z] == Sum[(- 1)^(k)Divide[(z)^(k),(k)!]BesselI[\[Nu]+ k, z], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [70 / 70] `{Plus[Complex[0.4358908643715884, -0.07192294931339177], Times[-1.0, NSum[Times[Power[-1, k], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[1.0679098760861825, 0.09257666026367889], Times[-1.0, NSum[Times[Power[-1, k], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], BesselI[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.44.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\tfrac{1}{2}z\right)^{\nu} = \sum_{k=0}^{\infty}(-1)^{k}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\modBesselI{\nu+2k}@{z}}	`((1)/(2)z)^(nu) = sum((- 1)^(k)((nu + 2k) GAMMA(nu + k))/(factorial(k))BesselI(nu + 2k, z), k = 0..infinity)`	`(Divide[1,2]z)^\[Nu] == Sum[(- 1)^(k)Divide[(\[Nu]+ 2k) Gamma[\[Nu]+ k],(k)!]BesselI[\[Nu]+ 2k, z], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Manual Skip!	Failed [7 / 7] `{Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1]}` `Plus[Complex[-0.2499999999999999, 0.43301270189221935], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 1]}`
10.44.E5	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}+2\sum_{k=1}^{\infty}\frac{\modBesselI{2k}@{z}}{k}}	`BesselK(0, z) = -(ln((1)/(2)z)+ gamma) BesselI(0, z)+ 2sum((BesselI(2k, z))/(k), k = 1..infinity)`	`BesselK[0, z] == -(Log[Divide[1,2]z]+ EulerGamma) BesselI[0, z]+ 2Sum[Divide[BesselI[2k, z],k], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
10.44.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{n}@{z} = \frac{n!(\tfrac{1}{2}z)^{-n}}{2}\sum_{k=0}^{n-1}(-1)^{k}\frac{(\tfrac{1}{2}z)^{k}\modBesselI{k}@{z}}{k!(n-k)}+(-1)^{n-1}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\modBesselI{n}@{z}+(-1)^{n}\sum_{k=1}^{\infty}\frac{(n+2k)\modBesselI{n+2k}@{z}}{k(n+k)}}	`BesselK(n, z) = (factorial(n)((1)/(2)z)^(- n))/(2)sum((- 1)^(k)(((1)/(2)z)^(k) BesselI(k, z))/(factorial(k)(n - k)), k = 0..n - 1)+(- 1)^(n - 1)(ln((1)/(2)z)- Psi(n + 1)) BesselI(n, z)+(- 1)^(n)* sum(((n + 2k) BesselI(n + 2k, z))/(k(n + k)), k = 1..infinity)`	`BesselK[n, z] == Divide[(n)!(Divide[1,2]z)^(- n),2]Sum[(- 1)^(k)Divide[(Divide[1,2]z)^(k) BesselI[k, z],(k)!(n - k)], {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n - 1)(Log[Divide[1,2]z]- PolyGamma[n + 1]) BesselI[n, z]+(- 1)^(n)* Sum[Divide[(n + 2k) BesselI[n + 2k, z],k(n + k)], {k, 1, Infinity}, GenerateConditions->None]`	Failure	Aborted	Manual Skip!	Failed [21 / 21] {Plus[Complex[1.084080291505059, -0.3914662527648858], NSum[Times[Power[k, -1], Power[Plus[1, k], -1], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]], Times[Complex[-0.8660254037844387, 0.49999999999999994], DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, 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[-1, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[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[Po
10.45.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}+(\nu^{2}-x^{2})w = 0}	`(x)^(2)* diff(w, [x$(2)])+ xdiff(w, x)+((nu)^(2)- (x)^(2)) w = 0`	`(x)^(2)* D[w, {x, 2}]+ xD[w, x]+(\[Nu]^(2)- (x)^(2)) w == 0`	Failure	Failure	Failed [240 / 300] `240/300]: [[-1.948557159-.1249999996I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 3/2}` `-.2165063507+.8750000006I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 1/2}`	Failed [240 / 300] `{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[1, 6]], Pi]]]}` `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[2, 3]], Pi]]]}`
10.45.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{\nu}@{x} = \realpart@{\modBesselI{i\nu}@{x}}}	`Re(BesselI(I(nu), x)) = Re(BesselI(Inu, x))`	`Re[BesselI[I\[Nu], x]] == Re[BesselI[I\[Nu], x]]`	Successful	Successful	-	Successful [Tested: 30]
10.45.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{\nu}@{x} = \modBesselK{i\nu}@{x}}	`BesselK(I(nu), x) = BesselK(Inu, x)`	`BesselK[I\[Nu], x] == BesselK[I\[Nu], x]`	Successful	Successful	-	Successful [Tested: 30]
10.45.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselIimag{-\nu}@{x} = \modBesselIimag{\nu}@{x}}	`Re(BesselI(I(- nu), x)) = Re(BesselI(I(nu), x))`	`Re[BesselI[I- \[Nu], x]] == Re[BesselI[I\[Nu], x]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.45.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modBesselKimag{-\nu}@{x} = \modBesselKimag{\nu}@{x}}	`BesselK(I(- nu), x) = BesselK(I(nu), x)`	`BesselK[I- \[Nu], x] == BesselK[I\[Nu], x]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.45.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modBesselKimag{\nu}@{x},\modBesselIimag{\nu}@{x}} = 1/x}	`(BesselK(I(nu), x))diff(Re(BesselI(I(nu), x)), x)-diff(BesselK(I(nu), x), x)(Re(BesselI(I(nu), x))) = 1/ x`	`Wronskian[{BesselK[I\[Nu], x], Re[BesselI[I\[Nu], x]]}, x] == 1/ x`	Failure	Failure	Error	Failed [30 / 30] `{Plus[-0.6666666666666666, Times[0.5, Plus[Complex[1.0700115379721733, -0.3754447148158467], Times[Complex[0.1636629185333998, 0.09141848176750039], Derivative[1][Re][Complex[2.445786867824693, 0.6492150843755028]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[-0.6666666666666666, Times[0.5, Plus[Complex[0.8415452902387464, 0.2726729041814867], Times[Complex[0.3412924192180222, 0.19179892830603273], Derivative[1][Re][Complex[1.3137906770541619, -0.7251169608509622]]]]]] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.45.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselKimag{0}@{x} = \modBesselK{0}@{x}}	`BesselK(I*(0), x) = BesselK(0, x)`	`BesselK[I*0, x] == BesselK[0, x]`	Successful	Successful	-	Successful [Tested: 3]
10.47.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}+\left(z^{2}-n(n+1)\right)w = 0}	`(z)^(2)* diff(w, [z$(2)])+ 2zdiff(w, z)+((z)^(2)- n(n + 1)) w = 0`	`(z)^(2)* D[w, {z, 2}]+ 2zD[w, z]+((z)^(2)- n(n + 1)) w == 0`	Failure	Failure	Failed [210 / 210] `210/210]: [[-1.732050808+.3733632160e-9I <- {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 1}` `-5.196152424-2.000000000I <- {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 2}`	Failed [210 / 210] `{Complex[-1.7320508075688772, 1.1102230246251565*^-16] <- {Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-5.196152422706633, -1.9999999999999996] <- {Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}-\left(z^{2}+n(n+1)\right)w = 0}	`(z)^(2)* diff(w, [z$(2)])+ 2zdiff(w, z)-((z)^(2)+ n(n + 1)) w = 0`	`(z)^(2)* D[w, {z, 2}]+ 2zD[w, z]-((z)^(2)+ n(n + 1)) w == 0`	Failure	Failure	Failed [210 / 210] `210/210]: [[-1.732050808-2.000000000I <- {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 1}` `-5.196152424-4.000000000I <- {w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 2}`	Failed [210 / 210] `{Complex[-1.7320508075688776, -1.9999999999999998] <- {Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-5.196152422706632, -3.9999999999999996] <- {Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z}}	`Error`	`SphericalBesselJ[n, z] == Sqrt[Divide[1,2]Pi/ z]BesselJ[n +Divide[1,2], z]`	Missing Macro Error	Failure	Skip - symbolical successful subtest	Successful [Tested: 21]
10.47.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z} = (-1)^{n}\sqrt{\tfrac{1}{2}\pi/z}\BesselY{-n-\frac{1}{2}}@{z}}	`sqrt((1)/(2)Pi/ z)BesselJ(n +(1)/(2), z) = (- 1)^(n)sqrt((1)/(2)Pi/ z)*BesselY(- n -(1)/(2), z)`	`Sqrt[Divide[1,2]Pi/ z]BesselJ[n +Divide[1,2], z] == (- 1)^(n)Sqrt[Divide[1,2]Pi/ z]*BesselY[- n -Divide[1,2], z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.47.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z}}	`Error`	`SphericalBesselY[n, z] == Sqrt[Divide[1,2]Pi/ z]BesselY[n +Divide[1,2], z]`	Missing Macro Error	Failure	Skip - symbolical successful subtest	Successful [Tested: 21]
10.47.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z} = (-1)^{n+1}\sqrt{\tfrac{1}{2}\pi/z}\BesselJ{-n-\frac{1}{2}}@{z}}	`sqrt((1)/(2)Pi/ z)BesselY(n +(1)/(2), z) = (- 1)^(n + 1)sqrt((1)/(2)Pi/ z)*BesselJ(- n -(1)/(2), z)`	`Sqrt[Divide[1,2]Pi/ z]BesselY[n +Divide[1,2], z] == (- 1)^(n + 1)Sqrt[Divide[1,2]Pi/ z]*BesselJ[- n -Divide[1,2], z]`	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
10.47.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z}}	`Error`	`SphericalHankelH1[n, z] == Sqrt[Divide[1,2]Pi/ z]HankelH1[n +Divide[1,2], z]`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.47.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z} = (-1)^{n+1}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{-n-\frac{1}{2}}@{z}}	`sqrt((1)/(2)Pi/ z)HankelH1(n +(1)/(2), z) = (- 1)^(n + 1)* Isqrt((1)/(2)Pi/ z)*HankelH1(- n -(1)/(2), z)`	`Sqrt[Divide[1,2]Pi/ z]HankelH1[n +Divide[1,2], z] == (- 1)^(n + 1)* ISqrt[Divide[1,2]Pi/ z]*HankelH1[- n -Divide[1,2], z]`	Successful	Failure	-	Successful [Tested: 21]
10.47.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z}}	`Error`	`SphericalHankelH2[n, z] == Sqrt[Divide[1,2]Pi/ z]HankelH2[n +Divide[1,2], z]`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.47.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z} = (-1)^{n}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{-n-\frac{1}{2}}@{z}}	`sqrt((1)/(2)Pi/ z)HankelH2(n +(1)/(2), z) = (- 1)^(n)* Isqrt((1)/(2)Pi/ z)*HankelH2(- n -(1)/(2), z)`	`Sqrt[Divide[1,2]Pi/ z]HankelH2[n +Divide[1,2], z] == (- 1)^(n)* ISqrt[Divide[1,2]Pi/ z]*HankelH2[- n -Divide[1,2], z]`	Successful	Failure	-	Successful [Tested: 21]
10.47.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{n+\frac{1}{2}}@{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n] == Sqrt[Divide[1,2]Pi/ z]*BesselI[n +Divide[1,2], z]`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{-n-\frac{1}{2}}@{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n] == Sqrt[Divide[1,2]Pi/ z]*BesselI[- n -Divide[1,2], z]`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[-0.41419719140728084, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.1065867555175597, 2.4569570135519543] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z}}	`Error`	`Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Sqrt[Divide[1,2]Pi/ z]BesselK[n +Divide[1,2], z]`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.47.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{-n-\frac{1}{2}}@{z}}	`sqrt((1)/(2)Pi/ z)BesselK(n +(1)/(2), z) = sqrt((1)/(2)Pi/ z)BesselK(- n -(1)/(2), z)`	`Sqrt[Divide[1,2]Pi/ z]BesselK[n +Divide[1,2], z] == Sqrt[Divide[1,2]Pi/ z]BesselK[- n -Divide[1,2], z]`	Successful	Successful	-	Successful [Tested: 21]
10.47#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \sphBesselJ{n}@{z}+i\sphBesselY{n}@{z}}	`Error`	`SphericalHankelH1[n, z] == SphericalBesselJ[n, z]+ I*SphericalBesselY[n, z]`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.47#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \sphBesselJ{n}@{z}-i\sphBesselY{n}@{z}}	`Error`	`SphericalHankelH2[n, z] == SphericalBesselJ[n, z]- I*SphericalBesselY[n, z]`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.47.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = (-1)^{n+1}\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}-\modsphBesseli{2}{n}@{z}\right)}	`Error`	`Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n + 1)Divide[1,2]Pi(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n]- Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[-0.7569924845794465, -0.925635877692591] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-1.0316385731075524, -4.1588442590402455] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = i^{-n}\sphBesselJ{n}@{iz}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n] == (I)^(- n) SphericalBesselJ[n, I*z]`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[0.06771919180965624, -0.2957981693651618] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.44982524194021284, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = i^{-n-1}\sphBesselY{n}@{iz}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n] == (I)^(- n - 1) SphericalBesselY[n, I*z]`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[-0.41419719140728045, -0.8850762711170859] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.1065867555175588, 2.456957013551956] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.47.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz}}	`Error`	`Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == -Divide[1,2]Pi(I)^(n)* SphericalHankelH1[n, I*z]`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.47.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz} = -\tfrac{1}{2}\pi i^{-n}\sphHankelh{2}{n}@{-iz}}	`Error`	`-Divide[1,2]Pi(I)^(n)* SphericalHankelH1[n, Iz] == -Divide[1,2]Pi(I)^(- n) SphericalHankelH2[n, - I*z]`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.47.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphBesselJ{n}@{-z} = (-1)^{n}\sphBesselJ{n}@{z}}	`Error`	`SphericalBesselJ[n, - z] == (- 1)^(n)* SphericalBesselJ[n, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.47.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphBesselY{n}@{-z} = (-1)^{n+1}\sphBesselY{n}@{z}}	`Error`	`SphericalBesselY[n, - z] == (- 1)^(n + 1)* SphericalBesselY[n, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.47.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphHankelh{1}{n}@{-z} = (-1)^{n}\sphHankelh{2}{n}@{z}}	`Error`	`SphericalHankelH1[n, - z] == (- 1)^(n)* SphericalHankelH2[n, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.47.E15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\sphHankelh{2}{n}@{-z} = (-1)^{n}\sphHankelh{1}{n}@{z}}	`Error`	`SphericalHankelH2[n, - z] == (- 1)^(n)* SphericalHankelH1[n, z]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.47.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modsphBesseli{1}{n}@{-z} = (-1)^{n}\modsphBesseli{1}{n}@{z}}	`Error`	`Sqrt[Divide[Pi, - z]/2] BesselI[(-1)^(1-1)(n + 1/2), n] == (- 1)^(n) Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.47.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \displaystyle\modsphBesseli{2}{n}@{-z} = (-1)^{n+1}\modsphBesseli{2}{n}@{z}}	`Error`	`Sqrt[Divide[Pi, - z]/2] BesselI[(-1)^(2-1)(n + 1/2), n] == (- 1)^(n + 1) Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.47.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{-z} = -\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}+\modsphBesseli{2}{n}@{z}\right)}	`Error`	`Sqrt[1/2 Pi /- z] BesselK[n + 1/2, - z] == -Divide[1,2]Pi(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n]+ Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n])`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[-0.5442463690831921, -1.8549132335154932] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[2.444806248586177, 3.5599138449204935] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}}	`Error`	`SphericalBesselJ[n, z] == Sin[z -Divide[1,2]nPi]Sum[(- 1)^(k)Divide[Subscript[a, 2k](n +Divide[1,2]),(z)^(2k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Cos[z -Divide[1,2]nPi]Sum[(- 1)^(k)Divide[Subscript[a, 2k + 1](n +Divide[1,2]),(z)^(2k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.49#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}@{z} = \frac{\sin@@{z}}{z}}	`Error`	`SphericalBesselJ[0, z] == Divide[Sin[z],z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{1}@{z} = \frac{\sin@@{z}}{z^{2}}-\frac{\cos@@{z}}{z}}	`Error`	`SphericalBesselJ[1, z] == Divide[Sin[z],(z)^(2)]-Divide[Cos[z],z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{2}@{z} = \left(-\frac{1}{z}+\frac{3}{z^{3}}\right)\sin@@{z}-\frac{3}{z^{2}}\cos@@{z}}	`Error`	`SphericalBesselJ[2, z] == (-Divide[1,z]+Divide[3,(z)^(3)])* Sin[z]-Divide[3,(z)^(2)]*Cos[z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}}	`Error`	`SphericalBesselY[n, z] == - Cos[z -Divide[1,2]nPi]Sum[(- 1)^(k)Divide[Subscript[a, 2k](n +Divide[1,2]),(z)^(2k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[z -Divide[1,2]nPi]Sum[(- 1)^(k)Divide[Subscript[a, 2k + 1](n +Divide[1,2]),(z)^(2k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.49#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{0}@{z} = -\frac{\cos@@{z}}{z}}	`Error`	`SphericalBesselY[0, z] == -Divide[Cos[z],z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{1}@{z} = -\frac{\cos@@{z}}{z^{2}}-\frac{\sin@@{z}}{z}}	`Error`	`SphericalBesselY[1, z] == -Divide[Cos[z],(z)^(2)]-Divide[Sin[z],z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{2}@{z} = \left(\frac{1}{z}-\frac{3}{z^{3}}\right)\cos@@{z}-\frac{3}{z^{2}}\sin@@{z}}	`Error`	`SphericalBesselY[2, z] == (Divide[1,z]-Divide[3,(z)^(3)])* Cos[z]-Divide[3,(z)^(2)]*Sin[z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = e^{iz}\sum_{k=0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}}	`Error`	`SphericalHankelH1[n, z] == Exp[Iz]Sum[(I)^(k - n - 1)Divide[Subscript[a, k](n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [210 / 210] `{Complex[-0.3966692432410339, 0.7497610210111748] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.3157223500929769, 0.5313692545383957] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = e^{-iz}\sum_{k=0}^{n}(-i)^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}}	`Error`	`SphericalHankelH2[n, z] == Exp[- Iz]Sum[(- I)^(k - n - 1)Divide[Subscript[a, k](n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.49.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n+1}\*\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n] == Divide[1,2]Exp[z]Sum[(- 1)^(k)Divide[Subscript[a, k](n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n + 1)Divide[1,2](E)^(- z) Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.49#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{0}@{z} = \frac{\sinh@@{z}}{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(0 + 1/2), 0] == Divide[Sinh[z],z]`	Missing Macro Error	Failure	-	Failed [7 / 7] `{Complex[-1.0789668887893185, -0.15155203743332835] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.9126970224666039, 0.13712305377128448] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.49#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{1}@{z} = -\frac{\sinh@@{z}}{z^{2}}+\frac{\cosh@@{z}}{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(1 + 1/2), 1] == -Divide[Sinh[z],(z)^(2)]+Divide[Cosh[z],z]`	Missing Macro Error	Failure	-	Failed [7 / 7] `{Complex[0.06771919180965646, -0.2957981693651617] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.3178790653897484, -0.6062561841669247] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.49#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\sinh@@{z}-\frac{3}{z^{2}}\cosh@@{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)]) Sinh[z]-Divide[3,(z)^(2)]*Cosh[z]`	Missing Macro Error	Failure	-	Failed [6 / 7] `{Complex[0.44982524194021334, -0.19064547195046933] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.2843828483915114, -0.37732112452647515] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.49.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n}\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n] == Divide[1,2]Exp[z]Sum[(- 1)^(k)Divide[Subscript[a, k](n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n)Divide[1,2](E)^(- z) Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.49#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{0}@{z} = \frac{\cosh@@{z}}{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(0 + 1/2), 0] == Divide[Cosh[z],z]`	Missing Macro Error	Failure	-	Failed [7 / 7] `{DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.49#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{1}@{z} = -\frac{\cosh@@{z}}{z^{2}}+\frac{\sinh@@{z}}{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(1 + 1/2), 1] == -Divide[Cosh[z],(z)^(2)]+Divide[Sinh[z],z]`	Missing Macro Error	Failure	-	Failed [7 / 7] `{Complex[-0.41419719140728073, -0.8850762711170859] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-1.1181398580617885, 1.2868595835312289] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.49#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\cosh@@{z}-\frac{3}{z^{2}}\sinh@@{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)]) Cosh[z]-Divide[3,(z)^(2)]*Sinh[z]`	Missing Macro Error	Failure	-	Failed [6 / 7] `{Complex[1.106586755517561, 2.456957013551956] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-2.803584197807803, -1.2408087832280956] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.49.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \tfrac{1}{2}\pi e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}}	`Error`	`Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Divide[1,2]PiExp[- z]Sum[Divide[Subscript[a, k](n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [210 / 210] `{Complex[-1.0260307573251746, 0.0967341401667452] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-2.907697530268464, -0.43148595883398677] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{0}@{z} = \tfrac{1}{2}\pi\frac{e^{-z}}{z}}	`Error`	`Sqrt[1/2 Pi /z] BesselK[0 + 1/2, z] == Divide[1,2]PiDivide[Exp[- z],z]`	Missing Macro Error	Failure	-	Successful [Tested: 7]
10.49#Ex14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{1}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{1}{z^{2}}\right)}	`Error`	`Sqrt[1/2 Pi /z] BesselK[1 + 1/2, z] == Divide[1,2]PiExp[- z]*(Divide[1,z]+Divide[1,(z)^(2)])`	Missing Macro Error	Failure	-	Successful [Tested: 7]
10.49#Ex15	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{2}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{3}{z^{2}}+\frac{3}{z^{3}}\right)}	`Error`	`Sqrt[1/2 Pi /z] BesselK[2 + 1/2, z] == Divide[1,2]PiExp[- z]*(Divide[1,z]+Divide[3,(z)^(2)]+Divide[3,(z)^(3)])`	Missing Macro Error	Failure	-	Successful [Tested: 7]
10.49#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sin@@{z}}{z}}	`Error`	`(-Divide[1,z]D[(z)^(n)-Divide[1,z], z])^(n)*Divide[Sin[z],z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[0.28766324258243325, 0.13393934480402792] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.302013441049254, 0.9125931496973667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cos@@{z}}{z}}	`Error`	`SphericalBesselY[n, z] (-Divide[1,z]D[(z)^(n)-Divide[1,z], z])^(n)*Divide[Cos[z],z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[-0.9342001374760677, 0.968266641946737] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.14357960272401077, 3.9384338499123404] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49#Ex18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sinh@@{z}}{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n] (Divide[1,z]D[(z)^(n)Divide[1,z], z])^(n)Divide[Sinh[z],z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[0.35534425318828616, -0.09521420567684166] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.19008700336701606, 0.7298484499303669] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49#Ex19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cosh@@{z}}{z}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n] (Divide[1,z]D[(z)^(n)Divide[1,z], z])^(n)Divide[Cosh[z],z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[-0.3553442531882861, 0.09521420567684165] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.31198506093225176, 1.0184810034762684] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = (-1)^{n}\tfrac{1}{2}\pi z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{e^{-z}}{z}}	`Error`	`Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n)Divide[1,2](Divide[1,z]D[(z)^(n)Divide[1,z], z])^(n)*Divide[Exp[- z],z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[0.3593544107322247, -1.2247601267643444] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.45891810409859557, -4.100723067341411] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49.E18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}^{2}@{z}+\sphBesselY{n}^{2}@{z} = \sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}}	`Error`	`(SphericalBesselJ[n, z])^(2)+ (SphericalBesselY[n, z])^(2) == Sum[Divide[Subscript[s, k](n +Divide[1,2]),(z)^(2k + 2)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [210 / 210] `{Complex[-1.2990381056766571, 0.5179491924311224] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-9.999999999999996, 1.5358983848622398] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.49#Ex20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}^{2}@{z}+\sphBesselY{0}^{2}@{z} = z^{-2}}	`Error`	`(SphericalBesselJ[0, z])^(2)+ (SphericalBesselY[0, z])^(2) == (z)^(- 2)`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49#Ex21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{1}^{2}@{z}+\sphBesselY{1}^{2}@{z} = z^{-2}+z^{-4}}	`Error`	`(SphericalBesselJ[1, z])^(2)+ (SphericalBesselY[1, z])^(2) == (z)^(- 2)+ (z)^(- 4)`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49#Ex22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{2}^{2}@{z}+\sphBesselY{2}^{2}@{z} = z^{-2}+3z^{-4}+9z^{-6}}	`Error`	`(SphericalBesselJ[2, z])^(2)+ (SphericalBesselY[2, z])^(2) == (z)^(- 2)+ 3(z)^(- 4)+ 9(z)^(- 6)`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.49.E20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\modsphBesseli{1}{n}@{z}\right)^{2}-\left(\modsphBesseli{2}{n}@{z}\right)^{2} = (-1)^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}}	`Error`	`(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n])^(2)-(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n])^(2) == (- 1)^(n + 1)* Sum[(- 1)^(k)Divide[Subscript[s, k](n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [210 / 210] `{Complex[-1.299038105676658, -0.7500000000000001] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-0.35182282028742856, 0.20312500000000058] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.50#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\sphBesselJ{n}@{z},\sphBesselY{n}@{z}} = z^{-2}}	`Error`	`Wronskian[{SphericalBesselJ[n, z], SphericalBesselY[n, z]}, z] == (z)^(- 2)`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.50#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\sphHankelh{1}{n}@{z},\sphHankelh{2}{n}@{z}} = -2iz^{-2}}	`Error`	`Wronskian[{SphericalHankelH1[n, z], SphericalHankelH2[n, z]}, z] == - 2I(z)^(- 2)`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.50#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesseli{2}{n}@{z}} = (-1)^{n+1}z^{-2}}	`Error`	`Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n], Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n]}, z] == (- 1)^(n + 1)* (z)^(- 2)`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[-0.5000000000000001, 0.8660254037844386] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.5000000000000001, -0.8660254037844386] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.50#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesselK{n}@{z}} = \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\}	`Error`	`Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[0.5384915109869794, 1.7026856201657974] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-2.6544302063904848, -2.4451654315616667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.50#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\ = -\tfrac{1}{2}\pi z^{-2}}	`Error`	`Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == -Divide[1,2]Pi*(z)^(- 2)`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Complex[0.5161524079039588, -2.211692333258562] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[7.686727830477982, 4.996906619076774] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.50#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n+1}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+1}@{z} = z^{-2}}	`Error`	`SphericalBesselJ[n + 1, z]SphericalBesselY[n, z]- SphericalBesselJ[n, z]SphericalBesselY[n + 1, z] == (z)^(- 2)`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.50#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n+2}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+2}@{z} = (2n+3)z^{-3}}	`Error`	`SphericalBesselJ[n + 2, z]SphericalBesselY[n, z]- SphericalBesselJ[n, z]SphericalBesselY[n + 2, z] == (2n + 3) (z)^(- 3)`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.50.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{0}@{z}\sphBesselJ{n}@{z}+\sphBesselY{0}@{z}\sphBesselY{n}@{z} = \cos@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+2}}+\sin@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+3}}}	`Error`	`SphericalBesselJ[0, z]SphericalBesselJ[n, z]+ SphericalBesselY[0, z]SphericalBesselY[n, z] == Cos[Divide[1,2]nPi]Sum[(- 1)^(k)Divide[Subscript[a, 2k](n +Divide[1,2]),(z)^(2k + 2)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[Divide[1,2]nPi]Sum[(- 1)^(k)Divide[Subscript[a, 2k + 1](n +Divide[1,2]),(z)^(2k + 3)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.51#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{n-1}(z)+f_{n+1}(z) = ((2n+1)/z)f_{n}(z)}	`f[n - 1](z)+ f[n + 1](z) = ((2n + 1)/ z) f[n]*(z)`	`Subscript[f, n - 1](z)+ Subscript[f, n + 1](z) == ((2n + 1)/ z) Subscript[f, n]*(z)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.51#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{n+1}f_{n}(z)) = z^{n-m+1}f_{n-m}(z)}	`(diff((1)/(z), z))^(m)((z)^(n + 1) f[n](z)) = (z)^(n - m + 1) f[n - m]*(z)`	`(D[Divide[1,z], z])^(m)((z)^(n + 1) Subscript[f, n](z)) == (z)^(n - m + 1) Subscript[f, n - m]*(z)`	Failure	Failure	Error	Failed [288 / 300] `{Complex[-0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.51#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{-n}f_{n}(z)) = (-1)^{m}z^{-n-m}f_{n+m}(z)}	`(diff((1)/(z), z))^(m)((z)^(- n) f[n](z)) = (- 1)^(m) (z)^(- n - m)* f[n + m]*(z)`	`(D[Divide[1,z], z])^(m)((z)^(- n) Subscript[f, n](z)) == (- 1)^(m) (z)^(- n - m)* Subscript[f, n + m]*(z)`	Failure	Failure	Failed [288 / 300] `288/300]: [[1.366025403-.3660254033I <- {z = 1/23^(1/2)+1/2I, f[n] = 1/23^(1/2)+1/2I, f[n+m] = 1/23^(1/2)+1/2I, n = 1, m = 3}` `.9999999993-.9999999984I <- {z = 1/23^(1/2)+1/2I, f[n] = 1/23^(1/2)+1/2I, f[n+m] = 1/23^(1/2)+1/2I, n = 2, m = 3}`	Failed [288 / 300] `{Complex[0.1339745962155613, 0.49999999999999994] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.3660254037844386, 0.36602540378443865] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.51#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{n-1}(z)-g_{n+1}(z) = ((2n+1)/z)g_{n}(z)}	`g[n - 1](z)- g[n + 1](z) = ((2n + 1)/ z) g[n]*(z)`	`Subscript[g, n - 1](z)- Subscript[g, n + 1](z) == ((2n + 1)/ z) Subscript[g, n]*(z)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.51#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{n+1}g_{n}(z)) = z^{n-m+1}g_{n-m}(z)}	`(diff((1)/(z), z))^(m)((z)^(n + 1) g[n](z)) = (z)^(n - m + 1) g[n - m]*(z)`	`(D[Divide[1,z], z])^(m)((z)^(n + 1) Subscript[g, n](z)) == (z)^(n - m + 1) Subscript[g, n - m]*(z)`	Failure	Failure	Error	Failed [288 / 300] `{Complex[-0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.49999999999999994, -1.8660254037844388] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[Times[-1, m], n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.51#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{-n}g_{n}(z)) = z^{-n-m}g_{n+m}(z)}	`(diff((1)/(z), z))^(m)((z)^(- n) g[n](z)) = (z)^(- n - m) g[n + m]*(z)`	`(D[Divide[1,z], z])^(m)((z)^(- n) Subscript[g, n](z)) == (z)^(- n - m) Subscript[g, n + m]*(z)`	Failure	Failure	Failed [288 / 300] `288/300]: [[.3660254028+1.366025403I <- {z = 1/23^(1/2)+1/2I, g[n] = 1/23^(1/2)+1/2I, g[n+m] = 1/23^(1/2)+1/2I, n = 1, m = 3}` `.9999999987+.9999999996I <- {z = 1/23^(1/2)+1/2I, g[n] = 1/23^(1/2)+1/2I, g[n+m] = 1/23^(1/2)+1/2I, n = 2, m = 3}`	Failed [288 / 300] `{Complex[-1.8660254037844388, 0.49999999999999994] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[-1.3660254037844388, 1.3660254037844386] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.53.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}}	`Error`	`SphericalBesselJ[n, z] == (z)^(n)* Sum[Divide[(-Divide[1,2](z)^(2))^(k),(k)!(2n + 2k + 1)!!], {k, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.53.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{z} = -\frac{1}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(\frac{1}{2}z^{2})^{k}}{k!}+\frac{(-1)^{n+1}}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}}	`Error`	`SphericalBesselY[n, z] == -Divide[1,(z)^(n + 1)]Sum[Divide[(2n - 2k - 1)!!(Divide[1,2](z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[(- 1)^(n + 1),(z)^(n + 1)]Sum[Divide[(-Divide[1,2](z)^(2))^(k),(k)!(2k - 2n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Successful [Tested: 21]
10.53.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{1}{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n] == (z)^(n) Sum[Divide[(Divide[1,2](z)^(2))^(k),(k)!(2n + 2k + 1)!!], {k, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.53.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesseli{2}{n}@{z} = \frac{(-1)^{n}}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(-\frac{1}{2}z^{2})^{k}}{k!}+\frac{1}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}}	`Error`	`Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n + 1/2), n] == Divide[(- 1)^(n),(z)^(n + 1)]Sum[Divide[(2n - 2k - 1)!!(-Divide[1,2](z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[1,(z)^(n + 1)]Sum[Divide[(Divide[1,2](z)^(2))^(k),(k)!(2k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [20 / 21] `{Complex[-0.4141971914072808, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[1.1065867555175597, 2.456957013551954] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.54.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{z^{n}}{2^{n+1}n!}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2n+1}\diff{\theta}}	`Error`	`SphericalBesselJ[n, z] == Divide[(z)^(n),(2)^(n + 1)* (n)!]Integrate[Cos[zCos[\[Theta]]](Sin[\[Theta]])^(2n + 1), {\[Theta], 0, Pi}, GenerateConditions->None]`	Missing Macro Error	Successful	-	Successful [Tested: 21]
10.54.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{(-i)^{n}}{2}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\assLegendreP[]{n}@{\cos@@{\theta}}\sin@@{\theta}\diff{\theta}}	`Error`	`SphericalBesselJ[n, z] == Divide[(- I)^(n),2]Integrate[Exp[IzCos[\[Theta]]]LegendreP[n, 0, 3, Cos[\[Theta]]]*Sin[\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Successful [Tested: 21]
10.54.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{z} = \frac{\pi}{2}\int_{1}^{\infty}e^{-zt}\assLegendreP[]{n}@{t}\diff{t}}	`Error`	`Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Divide[Pi,2]Integrate[Exp[- zt]*LegendreP[n, 0, 3, t], {t, 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Skipped - Because timed out
10.54.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{z} = \frac{(-i)^{n+1}}{2\pi}\int_{i\infty}^{(-1+,1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}}	`Error`	`SphericalBesselJ[n, z] == Divide[(- I)^(n + 1),2Pi]Integrate[Exp[Izt]LegendreQ[n, 0, 3, t], {t, IInfinity, (- 1 + , 1 +)}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Error
10.54#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{1}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}}	`Error`	`SphericalHankelH1[n, z] == Divide[(- I)^(n + 1),Pi]Integrate[Exp[Izt]LegendreQ[n, 0, 3, t], {t, I*Infinity, (1 +)}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Error
10.54#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphHankelh{2}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(-1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}}	`Error`	`SphericalHankelH2[n, z] == Divide[(- I)^(n + 1),Pi]Integrate[Exp[Izt]LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 +)}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Error
10.56.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{\sqrt{z^{2}-2zt}}}{z} = \frac{\cos@@{z}}{z}+\sum_{n=1}^{\infty}\frac{t^{n}}{n!}\sphBesselJ{n-1}@{z}}	`Error`	`Divide[Cos[Sqrt[(z)^(2)- 2zt]],z] == Divide[Cos[z],z]+ Sum[Divide[(t)^(n),(n)!]*SphericalBesselJ[n - 1, z], {n, 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [42 / 42] `{Plus[Complex[-1.0653161526495918, 0.32810386977400907], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-1.8246723112251149, 0.13108435615091096], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.56.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{\sqrt{z^{2}-2zt}}}{z} = \frac{\sin@@{z}}{z}+\sum_{n=1}^{\infty}\frac{t^{n}}{n!}\sphBesselY{n-1}@{z}}	`Error`	`Divide[Sin[Sqrt[(z)^(2)- 2zt]],z] == Divide[Sin[z],z]+ Sum[Divide[(t)^(n),(n)!]*SphericalBesselY[n - 1, z], {n, 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Skipped - Because timed out
10.56.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cosh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\cosh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{1}{n-1}@{z}}	`Error`	`Divide[Cosh[Sqrt[(z)^(2)+ 2Izt]],z] == Divide[Cosh[z],z]+ Sum[Divide[(It)^(n),(n)!]Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [42 / 42] `{Plus[Complex[-0.13108435615091052, -1.8246723112251153], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-0.022834987510423566, -1.7127448295681993], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.56.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sinh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\sinh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{2}{n-1}@{z}}	`Error`	`Divide[Sinh[Sqrt[(z)^(2)+ 2Izt]],z] == Divide[Sinh[z],z]+ Sum[Divide[(It)^(n),(n)!]Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [42 / 42] `{Plus[Complex[-0.12983798012989667, -2.1935922908985273], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-1.4886830119296848, -1.839102010336905], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.56.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\exp@{-\sqrt{z^{2}+2izt}}}{z} = \frac{e^{-z}}{z}+\frac{2}{\pi}\sum_{n=1}^{\infty}\frac{(-it)^{n}}{n!}\modsphBesselK{n-1}@{z}}	`Error`	`Divide[Exp[-Sqrt[(z)^(2)+ 2Izt]],z] == Divide[Exp[- z],z]+Divide[2,Pi]Sum[Divide[(- It)^(n),(n)!]Sqrt[1/2 Pi /z] BesselK[n - 1 + 1/2, z], {n, 1, Infinity}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Skipped - Because timed out
10.57.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}'@{(n+\tfrac{1}{2})z} = \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}\BesselJ{n+\frac{1}{2}}'@{(n+\tfrac{1}{2})z}-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}\BesselJ{n+\frac{1}{2}}@{(n+\tfrac{1}{2})z}}	`Error`	`D[SphericalBesselJ[n, (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}] == Divide[(Pi)^(Divide[1,2]),((2n + 1)z)^(Divide[1,2])]D[BesselJ[n +Divide[1,2], (n +Divide[1,2]) z], {(n +Divide[1,2])* z, 1}]-Divide[(Pi)^(Divide[1,2]),((2n + 1)z)^(Divide[3,2])]BesselJ[n +Divide[1,2], (n +Divide[1,2]) z]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Plus[Complex[0.14653389603833195, -0.029869009956249915], Times[Complex[-0.988457695936884, 0.2648564413786163], D[Complex[0.36567703182522004, 0.24184221354059504] <- {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], D[Complex[0.425509744388485, 0.14219887983348967], {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[0.06710374092328811, 0.007963502819859997], Times[Complex[-0.7656560389588212, 0.20515691731902835], D[Complex[0.2637838125883578, 0.3348231997381719] <- {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], D[Complex[0.27065896459303473, 0.20224233103375913], {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.60.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{w}}{w} = -\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselY{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}}	`Error`	`Divide[Cos[w],w] == - Sum[(2n + 1) SphericalBesselJ[n, v]SphericalBesselY[n, u]LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [300 / 300] `{Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}` `Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}`
10.60.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{w}}{w} = \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselJ{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}}	`Error`	`Divide[Sin[w],w] == Sum[(2n + 1) SphericalBesselJ[n, v]SphericalBesselJ[n, u]LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [300 / 300] `{Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {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]}` `Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {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]}`
10.60.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{e^{-w}}{w} = \frac{2}{\pi}\sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{v}\modsphBesselK{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}}	`Error`	`Divide[Exp[- w],w] == Divide[2,Pi]Sum[(2n + 1)* Sqrt[Divide[Pi, v]/2] BesselI[(-1)^(1-1)(n + 1/2), n]Sqrt[1/2 Pi /u] BesselK[n + 1/2, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Skipped - Because timed out
10.60.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselJ{n}@{2z} = -n!z^{n+1}\sum_{k=0}^{n}\frac{2n-2k+1}{k!(2n-k+1)!}\sphBesselJ{n-k}@{z}\sphBesselY{n-k}@{z}}	`Error`	`SphericalBesselJ[n, 2z] == - (n)!(z)^(n + 1)* Sum[Divide[2n - 2k + 1,(k)!(2n - k + 1)!]SphericalBesselJ[n - k, z]SphericalBesselY[n - k, z], {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Failed [6 / 21] {Plus[0.3456774997623559, Times[2.25, Plus[Times[-2.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[-3, Times[-2, ], Times[2, 1]], Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[1, Times[-1, ], Times[2, 1]], Power[1.5, 2], []], Times[-1, Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[Times[-3, ], Times[-14, Power[, 2]], Times[-20, Power[, 3]], Times[-8, Power[, 4]], Times[14, , 1], Times[40, Power[, 2], 1], Times[24, Power[, 3], 1], Times[-20, , Power[1, 2]], Times[-24, Power[, 2], Power[1, 2]], Times[8, , Power[1, 3]], Times[-3, Power[1.5, 2]], Times[2, , Power[1.5, 2]], Times[4, Power[, 2], Power[1.5, 2]], Times[-4, 1, Power[1.5, 2]], Times[-8, , 1, Power[1.5, 2]], Times[4, Power[1, 2], Power[1.5, 2]]], [Plus[1, ]]], Times[, Plus[1, , Times[-2, 1]], Plus[3, Times[4, ], Times[4, , 1], Times[-4, Power[1, 2]]], Plus[3, Times[8, ], Times[4, Power[, 2]], Times[-8, 1], Times[-8, , 1], Times[
10.60.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sphBesselY{n}@{2z} = n!z^{n+1}\sum_{k=0}^{n}\frac{n-k+\frac{1}{2}}{k!(2n-k+1)!}{\left(\sphBesselJ{n-k}^{2}@{z}-\sphBesselY{n-k}^{2}@{z}\right)}}	`Error`	`SphericalBesselY[n, 2z] == (n)!(z)^(n + 1)* Sum[Divide[n - k +Divide[1,2],(k)!(2n - k + 1)!]*((SphericalBesselJ[n - k, z])^(2)- (SphericalBesselY[n - k, z])^(2)), {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Failed [6 / 21] {Plus[0.06295916360231597, Times[-1.125, Plus[Times[-2.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[-3, Times[-2, ], Times[2, 1]], Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[1, Times[-1, ], Times[2, 1]], Power[1.5, 2], []], Times[-1, Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[Times[-3, ], Times[-14, Power[, 2]], Times[-20, Power[, 3]], Times[-8, Power[, 4]], Times[14, , 1], Times[40, Power[, 2], 1], Times[24, Power[, 3], 1], Times[-20, , Power[1, 2]], Times[-24, Power[, 2], Power[1, 2]], Times[8, , Power[1, 3]], Times[-3, Power[1.5, 2]], Times[2, , Power[1.5, 2]], Times[4, Power[, 2], Power[1.5, 2]], Times[-4, 1, Power[1.5, 2]], Times[-8, , 1, Power[1.5, 2]], Times[4, Power[1, 2], Power[1.5, 2]]], [Plus[1, ]]], Times[, Plus[1, , Times[-2, 1]], Plus[3, Times[4, ], Times[4, , 1], Times[-4, Power[1, 2]]], Plus[3, Times[8, ], Times[4, Power[, 2]], Times[-8, 1], Times[-8, , 1], Tim
10.60.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modsphBesselK{n}@{2z} = \frac{1}{\pi}n!z^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{2n-2k+1}{k!(2n-k+1)!}\modsphBesselK{n-k}^{2}@{z}}	`Error`	`Sqrt[1/2 Pi /2z] BesselK[n + 1/2, 2z] == Divide[1,Pi](n)!(z)^(n + 1)* Sum[(- 1)^(k)Divide[2n - 2k + 1,(k)!(2n - k + 1)!](Sqrt[1/2 Pi /z] BesselK[n - k + 1/2, z])^(2), {k, 0, n}, GenerateConditions->None]`	Missing Macro Error	Aborted	-	Failed [21 / 21] `{Complex[0.10365998143807895, 0.01421463603104145] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.21384035370849797, -0.0374061947505589] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}`
10.60.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{iz\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)i^{n}\sphBesselJ{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}}	`Error`	`Exp[IzCos[\[Alpha]]] == Sum[(2n + 1) (I)^(n)* SphericalBesselJ[n, z]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Plus[Complex[0.9634389243184156, 0.05909441627762202], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}` `Plus[Complex[0.46738148067268087, 0.44423123280344756], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}`
10.60.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}}	`Error`	`Exp[zCos[\[Alpha]]] == Sum[(2n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n]LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Plus[Complex[1.0625106169893304, 0.037595191618525974], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}` `Plus[Complex[1.935725445820811, 0.9084451535292719], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}`
10.60.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}}	`Error`	`Exp[- zCos[\[Alpha]]] == Sum[(- 1)^(n)(2n + 1) Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)(n + 1/2), n]LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Plus[Complex[0.939990215282077, -0.03326000860415312], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}` `Plus[Complex[0.4233587200353881, -0.19868425982147583], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}`
10.60.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{0}@{z\sin@@{\alpha}} = \sum_{n=0}^{\infty}(4n+1)\frac{(2n)!}{2^{2n}(n!)^{2}}\sphBesselJ{2n}@{z}\assLegendreP[]{2n}@{\cos@@{\alpha}}}	`Error`	`BesselJ[0, zSin[\[Alpha]]] == Sum[(4n + 1)Divide[(2n)!,(2)^(2n)((n)!)^(2)]SphericalBesselJ[2n, z]LegendreP[2n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]`	Missing Macro Error	Failure	-	Failed [21 / 21] `{Plus[Complex[0.8683151459050518, -0.20203213835937428], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.0707372016677029], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}` `Plus[Complex[0.9708614168197589, -0.04904886793011446], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.8775825618903728], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}`
10.60.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\sphBesselJ{n}^{2}@{z} = \frac{\sinint@{2z}}{2z}}	`Error`	`Sum[(SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[SinIntegral[2z],2z]`	Missing Macro Error	Successful	-	Successful [Tested: 7]
10.60.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}^{2}@{z} = 1}	`Error`	`Sum[(2n + 1) (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == 1`	Missing Macro Error	Failure	-	Failed [7 / 7] `{Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.60.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\sphBesselJ{n}^{2}@{z} = \frac{\sin@{2z}}{2z}}	`Error`	`Sum[(- 1)^(n)(2n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[Sin[2z],2z]`	Missing Macro Error	Failure	-	Failed [7 / 7] `{Plus[Complex[-0.6123335037567501, 0.46246896224791606], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[-1.2536290109103816, -0.6921871649112455], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.60.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}(2n+1)(\sphBesselJ{n}'@{z})^{2} = \tfrac{1}{3}}	`Error`	`Sum[(2n + 1)(D[SphericalBesselJ[n, z], {z, 1}])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[1,3]`	Missing Macro Error	Aborted	-	Skipped - Because timed out
10.61.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \BesselJ{\nu}@{xe^{3\pi i/4}}}	`KelvinBer(nu, x)+ IKelvinBei(nu, x) = BesselJ(nu, xexp(3PiI/ 4))`	`KelvinBer[\[Nu], x]+ IKelvinBei[\[Nu], x] == BesselJ[\[Nu], xExp[3PiI/ 4]]`	Successful	Failure	Skip - symbolical successful subtest	Successful [Tested: 30]
10.61.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\nu}@{xe^{3\pi i/4}} = e^{\nu\pi i}\BesselJ{\nu}@{xe^{-\pi i/4}}}	`BesselJ(nu, xexp(3PiI/ 4)) = exp(nuPiI)BesselJ(nu, xexp(- PiI/ 4))`	`BesselJ[\[Nu], xExp[3PiI/ 4]] == Exp[\[Nu]PiI]BesselJ[\[Nu], xExp[- PiI/ 4]]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\nu\pi i}\BesselJ{\nu}@{xe^{-\pi i/4}} = e^{\nu\pi i/2}\modBesselI{\nu}@{xe^{\pi i/4}}}	`exp(nuPiI)BesselJ(nu, xexp(- PiI/ 4)) = exp(nuPiI/ 2)BesselI(nu, xexp(PiI/ 4))`	`Exp[\[Nu]PiI]BesselJ[\[Nu], xExp[- PiI/ 4]] == Exp[\[Nu]PiI/ 2]BesselI[\[Nu], xExp[PiI/ 4]]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\nu\pi i/2}\modBesselI{\nu}@{xe^{\pi i/4}} = e^{3\nu\pi i/2}\modBesselI{\nu}@{xe^{-3\pi i/4}}}	`exp(nuPiI/ 2)BesselI(nu, xexp(PiI/ 4)) = exp(3nuPiI/ 2)BesselI(nu, xexp(- 3PiI/ 4))`	`Exp[\[Nu]PiI/ 2]BesselI[\[Nu], xExp[PiI/ 4]] == Exp[3\[Nu]PiI/ 2]BesselI[\[Nu], xExp[- 3PiI/ 4]]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{\nu}@@{x}+i\Kelvinkei{\nu}@@{x} = e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}}}	`KelvinKer(nu, x)+ IKelvinKei(nu, x) = exp(- nuPiI/ 2)BesselK(nu, xexp(PiI/ 4))`	`KelvinKer[\[Nu], x]+ IKelvinKei[\[Nu], x] == Exp[- \[Nu]PiI/ 2]BesselK[\[Nu], xExp[PiI/ 4]]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}} = \tfrac{1}{2}\pi i\HankelH{1}{\nu}@{xe^{3\pi i/4}}}	`exp(- nuPiI/ 2)BesselK(nu, xexp(PiI/ 4)) = (1)/(2)PiIHankelH1(nu, xexp(3Pi*I/ 4))`	`Exp[- \[Nu]PiI/ 2]BesselK[\[Nu], xExp[PiI/ 4]] == Divide[1,2]PiIHankelH1[\[Nu], xExp[3Pi*I/ 4]]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}\pi i\HankelH{1}{\nu}@{xe^{3\pi i/4}} = -\tfrac{1}{2}\pi ie^{-\nu\pi i}\HankelH{2}{\nu}@{xe^{-\pi i/4}}}	`(1)/(2)PiIHankelH1(nu, xexp(3PiI/ 4)) = -(1)/(2)PiIexp(- nuPiI)HankelH2(nu, xexp(- PiI/ 4))`	`Divide[1,2]PiIHankelH1[\[Nu], xExp[3PiI/ 4]] == -Divide[1,2]PiIExp[- \[Nu]PiI]HankelH2[\[Nu], xExp[- PiI/ 4]]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61.E3	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}-(ix^{2}+\nu^{2})w = 0}	`(x)^(2)* diff(w, [x$(2)])+ xdiff(w, x)-(I(x)^(2)+ (nu)^(2))* w = 0`	`(x)^(2)* D[w, {x, 2}]+ xD[w, x]-(I(x)^(2)+ \[Nu]^(2))* w == 0`	Failure	Failure	Failed [300 / 300] `300/300]: [[1.125000000-2.948557160I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 3/2}` `.1249999997-1.216506352I <- {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, x = 1/2}`	Failed [300 / 300] `{Complex[1.1249999999999996, -2.948557158514987] <- {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[1.1249999999999996, -0.9485571585149869] <- {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]]]}`
10.61.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x^{4}\deriv[4]{w}{x}+2x^{3}\deriv[3]{w}{x}-(1+2\nu^{2})\left(x^{2}\deriv[2]{w}{x}-x\deriv{w}{x}\right)+(\nu^{4}-4\nu^{2}+x^{4})w = 0}	`(x)^(4)* diff(w, [x$(4)])+ 2(x)^(3) diff(w, [x$(3)])-(1 + 2(nu)^(2))((x)^(2)* diff(w, [x$(2)])- xdiff(w, x))+((nu)^(4)- 4(nu)^(2)+ (x)^(4))* w = 0`	`(x)^(4)* D[w, {x, 4}]+ 2(x)^(3) D[w, {x, 3}]-(1 + 2\[Nu]^(2))((x)^(2)* D[w, {x, 2}]- xD[w, x])+(\[Nu]^(4)- 4\[Nu]^(2)+ (x)^(4))* w == 0`	Error	Failure	-	Skip - No test values generated
10.61#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{-x} = (-1)^{n}\Kelvinber{n}@@{x}}	`KelvinBer(n, - x) = (- 1)^(n)* KelvinBer(n, x)`	`KelvinBer[n, - x] == (- 1)^(n)* KelvinBer[n, x]`	Successful	Failure	-	Successful [Tested: 9]
10.61#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{-x} = (-1)^{n}\Kelvinbei{n}@@{x}}	`KelvinBei(n, - x) = (- 1)^(n)* KelvinBei(n, x)`	`KelvinBei[n, - x] == (- 1)^(n)* KelvinBei[n, x]`	Successful	Failure	-	Successful [Tested: 9]
10.61#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-\nu}@@{x} = \cos@{\nu\pi}\Kelvinber{\nu}@@{x}+\sin@{\nu\pi}\Kelvinbei{\nu}@@{x}+(2/\pi)\sin@{\nu\pi}\Kelvinker{\nu}@@{x}}	`KelvinBer(- nu, x) = cos(nuPi)KelvinBer(nu, x)+ sin(nuPi)KelvinBei(nu, x)+(2/ Pi)* sin(nuPi)KelvinKer(nu, x)`	`KelvinBer[- \[Nu], x] == Cos[\[Nu]Pi]KelvinBer[\[Nu], x]+ Sin[\[Nu]Pi]KelvinBei[\[Nu], x]+(2/ Pi)* Sin[\[Nu]Pi]KelvinKer[\[Nu], x]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{-\nu}@@{x} = -\sin@{\nu\pi}\Kelvinber{\nu}@@{x}+\cos@{\nu\pi}\Kelvinbei{\nu}@@{x}+(2/\pi)\sin@{\nu\pi}\Kelvinkei{\nu}@@{x}}	`KelvinBei(- nu, x) = - sin(nuPi)KelvinBer(nu, x)+ cos(nuPi)KelvinBei(nu, x)+(2/ Pi)* sin(nuPi)KelvinKei(nu, x)`	`KelvinBei[- \[Nu], x] == - Sin[\[Nu]Pi]KelvinBer[\[Nu], x]+ Cos[\[Nu]Pi]KelvinBei[\[Nu], x]+(2/ Pi)* Sin[\[Nu]Pi]KelvinKei[\[Nu], x]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.61#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{-\nu}@@{x} = \cos@{\nu\pi}\Kelvinker{\nu}@@{x}-\sin@{\nu\pi}\Kelvinkei{\nu}@@{x}}	`KelvinKer(- nu, x) = cos(nuPi)KelvinKer(nu, x)- sin(nuPi)KelvinKei(nu, x)`	`KelvinKer[- \[Nu], x] == Cos[\[Nu]Pi]KelvinKer[\[Nu], x]- Sin[\[Nu]Pi]KelvinKei[\[Nu], x]`	Successful	Failure	-	Successful [Tested: 30]
10.61#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{-\nu}@@{x} = \sin@{\nu\pi}\Kelvinker{\nu}@@{x}+\cos@{\nu\pi}\Kelvinkei{\nu}@@{x}}	`KelvinKei(- nu, x) = sin(nuPi)KelvinKer(nu, x)+ cos(nuPi)KelvinKei(nu, x)`	`KelvinKei[- \[Nu], x] == Sin[\[Nu]Pi]KelvinKer[\[Nu], x]+ Cos[\[Nu]Pi]KelvinKei[\[Nu], x]`	Successful	Failure	-	Successful [Tested: 30]
10.61#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-n}@@{x} = (-1)^{n}\Kelvinber{n}@@{x},~{}\Kelvinbei{-n}@@{x}}	`KelvinBer(- n, x) = (- 1)^(n)* KelvinBer(n, x),*KelvinBei(- n, x)`	`KelvinBer[- n, x] == (- 1)^(n)* KelvinBer[n, x],*KelvinBei[- n, x]`	Error	Failure	-	Error
10.61#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\Kelvinber{n}@@{x},~{}\Kelvinbei{-n}@@{x} = (-1)^{n}\Kelvinbei{n}@@{x}}	`(- 1)^(n)* KelvinBer(n, x),KelvinBei(- n, x) = (- 1)^(n) KelvinBei(n, x)`	`(- 1)^(n)* KelvinBer[n, x],KelvinBei[- n, x] == (- 1)^(n) KelvinBei[n, x]`	Error	Failure	-	Error
10.61#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{-n}@@{x} = (-1)^{n}\Kelvinker{n}@@{x},~{}\Kelvinkei{-n}@@{x}}	`KelvinKer(- n, x) = (- 1)^(n)* KelvinKer(n, x),*KelvinKei(- n, x)`	`KelvinKer[- n, x] == (- 1)^(n)* KelvinKer[n, x],*KelvinKei[- n, x]`	Error	Failure	-	Error
10.61#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{n}\Kelvinker{n}@@{x},~{}\Kelvinkei{-n}@@{x} = (-1)^{n}\Kelvinkei{n}@@{x}}	`(- 1)^(n)* KelvinKer(n, x),KelvinKei(- n, x) = (- 1)^(n) KelvinKei(n, x)`	`(- 1)^(n)* KelvinKer[n, x],KelvinKei[- n, x] == (- 1)^(n) KelvinKei[n, x]`	Error	Failure	-	Error
10.61#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos@{x+\frac{\pi}{8}}-e^{-x}\cos@{x-\frac{\pi}{8}}\right)}	`KelvinBer((1)/(2), xsqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pix))(exp(x)cos(x +(Pi)/(8))- exp(- x)*cos(x -(Pi)/(8)))`	`KelvinBer[Divide[1,2], xSqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pix]](Exp[x]Cos[x +Divide[Pi,8]]- Exp[- x]*Cos[x -Divide[Pi,8]])`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.61#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\sin@{x+\frac{\pi}{8}}+\,e^{-x}\sin@{x-\frac{\pi}{8}}\right)}	`KelvinBei((1)/(2), xsqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pix))(exp(x)sin(x +(Pi)/(8))+ exp(- x)*sin(x -(Pi)/(8)))`	`KelvinBei[Divide[1,2], xSqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pix]](Exp[x]Sin[x +Divide[Pi,8]]+ Exp[- x]*Sin[x -Divide[Pi,8]])`	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 3]
10.61#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{-\frac{1}{2}}@{x\sqrt{2}} = \frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\sin@{x+\frac{\pi}{8}}-e^{-x}\sin@{x-\frac{\pi}{8}}\right)}	`KelvinBer(-(1)/(2), xsqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pix))(exp(x)sin(x +(Pi)/(8))- exp(- x)*sin(x -(Pi)/(8)))`	`KelvinBer[-Divide[1,2], xSqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pix]](Exp[x]Sin[x +Divide[Pi,8]]- Exp[- x]*Sin[x -Divide[Pi,8]])`	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 3]
10.61#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{-\frac{1}{2}}@{x\sqrt{2}} = -\frac{2^{-\frac{3}{4}}}{\sqrt{\pi x}}\left(e^{x}\cos@{x+\frac{\pi}{8}}+e^{-x}\cos@{x-\frac{\pi}{8}}\right)}	`KelvinBei(-(1)/(2), xsqrt(2)) = -((2)^(-(3)/(4)))/(sqrt(Pix))(exp(x)cos(x +(Pi)/(8))+ exp(- x)*cos(x -(Pi)/(8)))`	`KelvinBei[-Divide[1,2], xSqrt[2]] == -Divide[(2)^(-Divide[3,4]),Sqrt[Pix]](Exp[x]Cos[x +Divide[Pi,8]]+ Exp[- x]*Cos[x -Divide[Pi,8]])`	Failure	Successful	Successful [Tested: 3]	Successful [Tested: 3]
10.61.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{\frac{1}{2}}@{x\sqrt{2}} = \Kelvinkei{-\frac{1}{2}}@{x\sqrt{2}}}	`KelvinKer((1)/(2), xsqrt(2)) = KelvinKei(-(1)/(2), xsqrt(2))`	`KelvinKer[Divide[1,2], xSqrt[2]] == KelvinKei[-Divide[1,2], xSqrt[2]]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 3]
10.61.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{-\frac{1}{2}}@{x\sqrt{2}} = -2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\sin@{x-\frac{\pi}{8}}}	`KelvinKei(-(1)/(2), xsqrt(2)) = - (2)^(-(3)/(4))sqrt((Pi)/(x))exp(- x)sin(x -(Pi)/(8))`	`KelvinKei[-Divide[1,2], xSqrt[2]] == - (2)^(-Divide[3,4])Sqrt[Divide[Pi,x]]Exp[- x]Sin[x -Divide[Pi,8]]`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.61.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{\frac{1}{2}}@{x\sqrt{2}} = -\Kelvinker{-\frac{1}{2}}@{x\sqrt{2}}}	`KelvinKei((1)/(2), xsqrt(2)) = - KelvinKer(-(1)/(2), xsqrt(2))`	`KelvinKei[Divide[1,2], xSqrt[2]] == - KelvinKer[-Divide[1,2], xSqrt[2]]`	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 3]
10.61.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\Kelvinker{-\frac{1}{2}}@{x\sqrt{2}} = -2^{-\frac{3}{4}}\sqrt{\frac{\pi}{x}}e^{-x}\cos@{x-\frac{\pi}{8}}}	`- KelvinKer(-(1)/(2), xsqrt(2)) = - (2)^(-(3)/(4))sqrt((Pi)/(x))exp(- x)cos(x -(Pi)/(8))`	`- KelvinKer[-Divide[1,2], xSqrt[2]] == - (2)^(-Divide[3,4])Sqrt[Divide[Pi,x]]Exp[- x]Cos[x -Divide[Pi,8]]`	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
10.63#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{\nu-1}(x)+f_{\nu+1}(x) = -(\nu\sqrt{2}/x)\left(f_{\nu}(x)-g_{\nu}(x)\right)}	`f[nu - 1](x)+ f[nu + 1](x) = -(nusqrt(2)/ x)(f[nu](x)- g[nu](x))`	`Subscript[f, \[Nu]- 1](x)+ Subscript[f, \[Nu]+ 1](x) == -(\[Nu]Sqrt[2]/ x)(Subscript[f, \[Nu]](x)- Subscript[g, \[Nu]](x))`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.63#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinber{}'@@{x} = \Kelvinber{1}@@{x}+\Kelvinbei{1}@@{x}}	`diff( KelvinBer(, x), x$(1) ) = KelvinBer(1, x)+ KelvinBei(1, x)`	`D[KelvinBer[, x], {x, 1}] == KelvinBer[1, x]+ KelvinBei[1, x]`	Error	Failure	-	Failed [3 / 3] `{Plus[0.297000428957679, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 1.5]], KelvinBei[Plus[1.0, Null], 1.5], Times[-1.0, KelvinBer[Plus[-1.0, Null], 1.5]], KelvinBer[Plus[1.0, Null], 1.5]]]] <- {Rule[x, 1.5]}` `Plus[0.011047944038096752, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 0.5]], KelvinBei[Plus[1.0, Null], 0.5], Times[-1.0, KelvinBer[Plus[-1.0, Null], 0.5]], KelvinBer[Plus[1.0, Null], 0.5]]]] <- {Rule[x, 0.5]}`
10.63#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinbei{}'@@{x} = -\Kelvinber{1}x+\Kelvinbei{1}x}	`diff( KelvinBei(, x), x$(1) ) = - KelvinBer(1, x)+ KelvinBei(1, x)`	`D[KelvinBei[, x], {x, 1}] == - KelvinBer[1, x]+ KelvinBei[1, x]`	Error	Failure	-	Failed [3 / 3] `{Plus[-1.0327304069618592, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 1.5]], KelvinBei[Plus[1.0, Null], 1.5], KelvinBer[Plus[-1.0, Null], 1.5], Times[-1.0, KelvinBer[Plus[1.0, Null], 1.5]]]]] <- {Rule[x, 1.5]}` `Plus[-0.35343830347212746, Times[0.35355339059327373, Plus[Times[-1.0, KelvinBei[Plus[-1.0, Null], 0.5]], KelvinBei[Plus[1.0, Null], 0.5], KelvinBer[Plus[-1.0, Null], 0.5], Times[-1.0, KelvinBer[Plus[1.0, Null], 0.5]]]]] <- {Rule[x, 0.5]}`
10.63#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinker{}'@@{x} = \Kelvinker{1}x+\Kelvinkei{1}x}	`diff( KelvinKer(, x), x$(1) ) = KelvinKer(1, x)+ KelvinKei(1, x)`	`D[KelvinKer[, x], {x, 1}] == KelvinKer[1, x]+ KelvinKei[1, x]`	Error	Failure	-	Failed [3 / 3] `{Plus[0.4160356041812476, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 1.5]], KelvinKei[Plus[1.0, Null], 1.5], Times[-1.0, KelvinKer[Plus[-1.0, Null], 1.5]], KelvinKer[Plus[1.0, Null], 1.5]]]] <- {Rule[x, 1.5]}` `Plus[2.5735854919446126, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 0.5]], KelvinKei[Plus[1.0, Null], 0.5], Times[-1.0, KelvinKer[Plus[-1.0, Null], 0.5]], KelvinKer[Plus[1.0, Null], 0.5]]]] <- {Rule[x, 0.5]}`
10.63#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2}\Kelvinkei{}'@@{x} = -\Kelvinker{1}x+\Kelvinkei{1}x}	`diff( KelvinKei(, x), x$(1) ) = - KelvinKer(1, x)+ KelvinKei(1, x)`	`D[KelvinKei[, x], {x, 1}] == - KelvinKer[1, x]+ KelvinKei[1, x]`	Error	Failure	-	Failed [3 / 3] `{Plus[-0.418052966151267, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 1.5]], KelvinKei[Plus[1.0, Null], 1.5], KelvinKer[Plus[-1.0, Null], 1.5], Times[-1.0, KelvinKer[Plus[1.0, Null], 1.5]]]]] <- {Rule[x, 1.5]}` `Plus[-0.47122132111956727, Times[0.35355339059327373, Plus[Times[-1.0, KelvinKei[Plus[-1.0, Null], 0.5]], KelvinKei[Plus[1.0, Null], 0.5], KelvinKer[Plus[-1.0, Null], 0.5], Times[-1.0, KelvinKer[Plus[1.0, Null], 0.5]]]]] <- {Rule[x, 0.5]}`
10.63#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu+1} = p_{\nu-1}-(4\nu/x)r_{\nu}}	`p[nu + 1] = p[nu - 1]-(4nu/ x) r[nu]`	`Subscript[p, \[Nu]+ 1] == Subscript[p, \[Nu]- 1]-(4\[Nu]/ x) Subscript[r, \[Nu]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.63#Ex18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{\nu+1} = -(\nu/x)p_{\nu}+r_{\nu}}	`q[nu + 1] = -(nu/ x)* p[nu]+ r[nu]`	`Subscript[q, \[Nu]+ 1] == -(\[Nu]/ x)* Subscript[p, \[Nu]]+ Subscript[r, \[Nu]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.63#Ex19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{\nu+1} = -((\nu+1)/x)p_{\nu+1}+q_{\nu}}	`r[nu + 1] = -((nu + 1)/ x)* p[nu + 1]+ q[nu]`	`Subscript[r, \[Nu]+ 1] == -((\[Nu]+ 1)/ x)* Subscript[p, \[Nu]+ 1]+ Subscript[q, \[Nu]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.63#Ex20	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}-(\nu^{2}/x^{2})p_{\nu}}	`s[nu] = (1)/(2)p[nu + 1]+(1)/(2)p[nu - 1]-((nu)^(2)/ (x)^(2))* p[nu]`	`Subscript[s, \[Nu]] == Divide[1,2]Subscript[p, \[Nu]+ 1]+Divide[1,2]Subscript[p, \[Nu]- 1]-(\[Nu]^(2)/ (x)^(2))* Subscript[p, \[Nu]]`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.63.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{\nu}s_{\nu} = r_{\nu}^{2}+q_{\nu}^{2}}	`p[nu]*s[nu] = (r[nu])^(2)+ (q[nu])^(2)`	`Subscript[p, \[Nu]]*Subscript[s, \[Nu]] == (Subscript[r, \[Nu]])^(2)+ (Subscript[q, \[Nu]])^(2)`	Skipped - no semantic math	Skipped - no semantic math	-	-
10.64.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}}	`KelvinBer(n, xsqrt(2)) = ((- 1)^(n))/(Pi)int(cos(xsin(t)- nt)cosh(xsin(t)), t = 0..Pi)`	`KelvinBer[n, xSqrt[2]] == Divide[(- 1)^(n),Pi]Integrate[Cos[xSin[t]- nt]Cosh[xSin[t]], {t, 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 9]	Skipped - Because timed out
10.64.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}}	`KelvinBei(n, xsqrt(2)) = ((- 1)^(n))/(Pi)int(sin(xsin(t)- nt)sinh(xsin(t)), t = 0..Pi)`	`KelvinBei[n, xSqrt[2]] == Divide[(- 1)^(n),Pi]Integrate[Sin[xSin[t]- nt]Sinh[xSin[t]], {t, 0, Pi}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 9]	Skipped - Because timed out
10.65#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\cos@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}}	`KelvinBer(nu, x) = ((1)/(2)x)^(nu) sum((cos((3)/(4)nuPi +(1)/(2)kPi))/(factorial(k)GAMMA(nu + k + 1))((1)/(4)*(x)^(2))^(k), k = 0..infinity)`	`KelvinBer[\[Nu], x] == (Divide[1,2]x)^\[Nu] Sum[Divide[Cos[Divide[3,4]\[Nu]Pi +Divide[1,2]kPi],(k)!Gamma[\[Nu]+ k + 1]](Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.65#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\sin@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}}	`KelvinBei(nu, x) = ((1)/(2)x)^(nu) sum((sin((3)/(4)nuPi +(1)/(2)kPi))/(factorial(k)GAMMA(nu + k + 1))((1)/(4)*(x)^(2))^(k), k = 0..infinity)`	`KelvinBei[\[Nu], x] == (Divide[1,2]x)^\[Nu] Sum[Divide[Sin[Divide[3,4]\[Nu]Pi +Divide[1,2]kPi],(k)!Gamma[\[Nu]+ k + 1]](Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
10.65#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{}@@{x} = 1-\frac{(\frac{1}{4}x^{2})^{2}}{(2!)^{2}}+\frac{(\frac{1}{4}x^{2})^{4}}{(4!)^{2}}-\dotsb}	`KelvinBer(, x) = 1 -(((1)/(4)(x)^(2))^(2))/((factorial(2))^(2))+(((1)/(4)(x)^(2))^(4))/((factorial(4))^(2))- ..`	`KelvinBer[, x] == 1 -Divide[(Divide[1,4](x)^(2))^(2),((2)!)^(2)]+Divide[(Divide[1,4](x)^(2))^(4),((4)!)^(2)]- \[Ellipsis]`	Error	Failure	-	Failed [3 / 3] `{Plus[-0.921072244644165, …, KelvinBer[Null, 1.5]] <- {Rule[x, 1.5]}` `Plus[-0.9990234639909532, …, KelvinBer[Null, 0.5]] <- {Rule[x, 0.5]}`
10.65#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{}@@{x} = \tfrac{1}{4}x^{2}-\frac{(\frac{1}{4}x^{2})^{3}}{(3!)^{2}}+\frac{(\frac{1}{4}x^{2})^{5}}{(5!)^{2}}-\dotsi}	`KelvinBei(, x) = (1)/(4)(x)^(2)-(((1)/(4)(x)^(2))^(3))/((factorial(3))^(2))+(((1)/(4)*(x)^(2))^(5))/((factorial(5))^(2))- ..`	`KelvinBei[, x] == Divide[1,4](x)^(2)-Divide[(Divide[1,4](x)^(2))^(3),((3)!)^(2)]+Divide[(Divide[1,4]*(x)^(2))^(5),((5)!)^(2)]- \[Ellipsis]`	Error	Failure	-	Failed [3 / 3] `{Plus[-0.5575600630044937, …, KelvinBei[Null, 1.5]] <- {Rule[x, 1.5]}` `Plus[-0.06249321838219961, …, KelvinBei[Null, 0.5]] <- {Rule[x, 0.5]}`
10.65.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{n}@@{x} = \tfrac{1}{2}(\tfrac{1}{2}x)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\cos@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}-\ln@{\tfrac{1}{2}x}\Kelvinber{n}@@{x}+\tfrac{1}{4}\pi\Kelvinbei{n}@@{x}+\tfrac{1}{2}(\tfrac{1}{2}x)^{n}\sum_{k=0}^{\infty}\frac{\digamma@{k+1}+\digamma@{n+k+1}}{k!(n+k)!}\cos@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}}	`KelvinKer(n, x) = (1)/(2)((1)/(2)x)^(- n)* sum((factorial(n - k - 1))/(factorial(k))cos((3)/(4)nPi +(1)/(2)kPi)((1)/(4)(x)^(2))^(k), k = 0..n - 1)- ln((1)/(2)x)KelvinBer(n, x)+(1)/(4)PiKelvinBei(n, x)+(1)/(2)((1)/(2)x)^(n) sum((Psi(k + 1)+ Psi(n + k + 1))/(factorial(k)factorial(n + k))cos((3)/(4)nPi +(1)/(2)kPi)((1)/(4)(x)^(2))^(k), k = 0..infinity)`	`KelvinKer[n, x] == Divide[1,2](Divide[1,2]x)^(- n)* Sum[Divide[(n - k - 1)!,(k)!]Cos[Divide[3,4]nPi +Divide[1,2]kPi](Divide[1,4](x)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]- Log[Divide[1,2]x]KelvinBer[n, x]+Divide[1,4]PiKelvinBei[n, x]+Divide[1,2](Divide[1,2]x)^(n) Sum[Divide[PolyGamma[k + 1]+ PolyGamma[n + k + 1],(k)!(n + k)!]Cos[Divide[3,4]nPi +Divide[1,2]kPi](Divide[1,4](x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Aborted	Skipped - Because timed out	Failed [9 / 9] `{Indeterminate <- {Rule[n, 1], Rule[x, 1.5]}` `Indeterminate <- {Rule[n, 2], Rule[x, 1.5]}`
10.65.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{n}@@{x} = -\tfrac{1}{2}(\tfrac{1}{2}x)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\sin@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}-\ln@{\tfrac{1}{2}x}\Kelvinbei{n}@@{x}-\tfrac{1}{4}\pi\Kelvinber{n}@@{x}+\tfrac{1}{2}(\tfrac{1}{2}x)^{n}\sum_{k=0}^{\infty}\frac{\digamma@{k+1}+\digamma@{n+k+1}}{k!(n+k)!}\sin@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}}	`KelvinKei(n, x) = -(1)/(2)((1)/(2)x)^(- n)* sum((factorial(n - k - 1))/(factorial(k))sin((3)/(4)nPi +(1)/(2)kPi)((1)/(4)(x)^(2))^(k), k = 0..n - 1)- ln((1)/(2)x)KelvinBei(n, x)-(1)/(4)PiKelvinBer(n, x)+(1)/(2)((1)/(2)x)^(n) sum((Psi(k + 1)+ Psi(n + k + 1))/(factorial(k)factorial(n + k))sin((3)/(4)nPi +(1)/(2)kPi)((1)/(4)(x)^(2))^(k), k = 0..infinity)`	`KelvinKei[n, x] == -Divide[1,2](Divide[1,2]x)^(- n)* Sum[Divide[(n - k - 1)!,(k)!]Sin[Divide[3,4]nPi +Divide[1,2]kPi](Divide[1,4](x)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]- Log[Divide[1,2]x]KelvinBei[n, x]-Divide[1,4]PiKelvinBer[n, x]+Divide[1,2](Divide[1,2]x)^(n) Sum[Divide[PolyGamma[k + 1]+ PolyGamma[n + k + 1],(k)!(n + k)!]Sin[Divide[3,4]nPi +Divide[1,2]kPi](Divide[1,4](x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]`	Aborted	Aborted	Skipped - Because timed out	Failed [9 / 9] `{Indeterminate <- {Rule[n, 1], Rule[x, 1.5]}` `Indeterminate <- {Rule[n, 2], Rule[x, 1.5]}`
10.65#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinker{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinber{}@@{x}+\tfrac{1}{4}\pi\Kelvinbei{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+1}}{((2k)!)^{2}}(\tfrac{1}{4}x^{2})^{2k}}	`KelvinBei(, x)+ sum((- 1)^(k)(Psi(2k + 1))/((factorial(2k))^(2))((1)/(4)(x)^(2))^(2k), k = 0..infinity)`	`KelvinBei[, x]+ Sum[(- 1)^(k)Divide[PolyGamma[2k + 1],((2k)!)^(2)](Divide[1,4](x)^(2))^(2k), {k, 0, Infinity}, GenerateConditions->None]`	Error	Aborted	-	Skipped - Because timed out
10.65#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinkei{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinbei{}@@{x}-\tfrac{1}{4}\pi\Kelvinber{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+2}}{((2k+1)!)^{2}}(\tfrac{1}{4}x^{2})^{2k+1}}	`KelvinBer(, x)+ sum((- 1)^(k)(Psi(2k + 2))/((factorial(2k + 1))^(2))((1)/(4)(x)^(2))^(2k + 1), k = 0..infinity)`	`KelvinBer[, x]+ Sum[(- 1)^(k)Divide[PolyGamma[2k + 2],((2k + 1)!)^(2)](Divide[1,4](x)^(2))^(2k + 1), {k, 0, Infinity}, GenerateConditions->None]`	Error	Failure	-	Failed [3 / 3] `{Plus[-0.23161280473545226, Times[-1.0, KelvinBer[Null, 1.5]], KelvinKei[Null, 1.5]] <- {Rule[x, 1.5]}` `Plus[-0.02641550246351669, Times[-1.0, KelvinBer[Null, 0.5]], KelvinKei[Null, 0.5]] <- {Rule[x, 0.5]}`
10.65.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x} = (\tfrac{1}{2}x)^{2\nu}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}}	`(KelvinBer(nu, x))^(2)+ (KelvinBei(nu, x))^(2) = ((1)/(2)x)^(2nu)* sum((1)/(GAMMA(nu + k + 1)GAMMA(nu + 2k + 1))(((1)/(4)(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity)`	`(KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2) == (Divide[1,2]x)^(2\[Nu])* Sum[Divide[1,Gamma[\[Nu]+ k + 1]Gamma[\[Nu]+ 2k + 1]]Divide[(Divide[1,4](x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None]`	Successful	Successful	-	Successful [Tested: 30]
10.65.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x} = (\tfrac{1}{2}x)^{2\nu+1}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+2}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}}	`KelvinBer(nu, x)diff( KelvinBei(nu, x), x$(1) )- diff( KelvinBer(nu, x), x$(1) )KelvinBei(nu, x) = ((1)/(2)x)^(2nu + 1)* sum((1)/(GAMMA(nu + k + 1)GAMMA(nu + 2k + 2))(((1)/(4)(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity)`	`KelvinBer[\[Nu], x]D[KelvinBei[\[Nu], x], {x, 1}]- D[KelvinBer[\[Nu], x], {x, 1}]KelvinBei[\[Nu], x] == (Divide[1,2]x)^(2\[Nu]+ 1)* Sum[Divide[1,Gamma[\[Nu]+ k + 1]Gamma[\[Nu]+ 2k + 2]]Divide[(Divide[1,4](x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Successful	Failed [21 / 30] `21/30]: [[.7271930e-3+.45983036e-2I <- {nu = 1/23^(1/2)+1/2I, x = 3/2}` `-.41528503e-2+.322695404e-1I <- {nu = 1/23^(1/2)+1/2I, x = 2}`	Failed [3 / 30] `{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}` `Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]}`
10.65.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}\Kelvinber{\nu}'@@{x}+\Kelvinbei{\nu}@@{x}\Kelvinbei{\nu}'@@{x} = \tfrac{1}{2}(\tfrac{1}{2}x)^{2\nu-1}\sum_{k=0}^{\infty}\frac{1}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}}	`KelvinBer(nu, x)diff( KelvinBer(nu, x), x$(1) )+ KelvinBei(nu, x)diff( KelvinBei(nu, x), x$(1) ) = (1)/(2)((1)/(2)x)^(2nu - 1) sum((1)/(GAMMA(nu + k + 1)GAMMA(nu + 2k))(((1)/(4)(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity)`	`KelvinBer[\[Nu], x]D[KelvinBer[\[Nu], x], {x, 1}]+ KelvinBei[\[Nu], x]D[KelvinBei[\[Nu], x], {x, 1}] == Divide[1,2](Divide[1,2]x)^(2\[Nu]- 1) Sum[Divide[1,Gamma[\[Nu]+ k + 1]Gamma[\[Nu]+ 2k]]Divide[(Divide[1,4](x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Successful	Failed [25 / 30] `25/30]: [[.71978298e-2-.3037583875e-1I <- {nu = 1/23^(1/2)+1/2I, x = 3/2}` `.607273780e-1-.1071579728I <- {nu = 1/23^(1/2)+1/2I, x = 2}`	Failed [3 / 30] `{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}` `Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]}`
10.65.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\Kelvinber{\nu}'@@{x}\right)^{2}+\left(\Kelvinbei{\nu}'@@{x}\right)^{2} = (\tfrac{1}{2}x)^{2\nu-2}\sum_{k=0}^{\infty}\frac{2k^{2}+2\nu k+\frac{1}{4}\nu^{2}}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}}	`(diff( KelvinBer(nu, x), x$(1) ))^(2)+(diff( KelvinBei(nu, x), x$(1) ))^(2) = ((1)/(2)x)^(2nu - 2)* sum((2(k)^(2)+ 2nuk +(1)/(4)(nu)^(2))/(GAMMA(nu + k + 1)GAMMA(nu + 2k + 1))(((1)/(4)(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity)`	`(D[KelvinBer[\[Nu], x], {x, 1}])^(2)+(D[KelvinBei[\[Nu], x], {x, 1}])^(2) == (Divide[1,2]x)^(2\[Nu]- 2)* Sum[Divide[2(k)^(2)+ 2\[Nu]k +Divide[1,4]\[Nu]^(2),Gamma[\[Nu]+ k + 1]Gamma[\[Nu]+ 2k + 1]]Divide[(Divide[1,4](x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Successful	Failed [3 / 30] `3/30]: [[Float(undefined)+Float(undefined)I <- {nu = -2, x = 3/2}` `Float(undefined)+Float(undefined)I <- {nu = -2, x = 1/2}`	Failed [3 / 30] `{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}` `Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]}`
10.66.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!}}	`KelvinBer(nu, x)+ IKelvinBei(nu, x) = sum((exp((3nu + k)* PiI/ 4)(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)`	`KelvinBer[\[Nu], x]+ IKelvinBei[\[Nu], x] == Sum[Divide[Exp[(3\[Nu]+ k)* PiI/ 4](x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [30 / 30] `{Plus[Complex[-0.12257968900025018, 0.2735107661041647], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Plus[Complex[0.3467793075651209, -0.08562995402477025], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`<
10.66.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}\modBesselI{\nu+k}@{x}}{2^{k/2}k!}}	`sum((exp((3nu + k) PiI/ 4)(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) = sum((exp((3nu + 3k)* PiI/ 4)(x)^(k)* BesselI(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)`	`Sum[Divide[Exp[(3\[Nu]+ k) PiI/ 4](x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None] == Sum[Divide[Exp[(3\[Nu]+ 3k)* PiI/ 4](x)^(k)* BesselI[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None]`	Failure	Failure	Skipped - Because timed out	Failed [30 / 30] {Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, k]], Pi]], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} `Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Times[`
10.66#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinber{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k}@{x}\modBesselI{2k}@{x}}	`KelvinBer(n, xsqrt(2)) = sum((- 1)^(n + k) BesselJ(n + 2k, x)BesselI(2*k, x), k = - infinity..infinity)`	`KelvinBer[n, xSqrt[2]] == Sum[(- 1)^(n + k) BesselJ[n + 2k, x]BesselI[2*k, x], {k, - Infinity, Infinity}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 9]	Skipped - Because timed out
10.66#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kelvinbei{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k+1}@{x}\modBesselI{2k+1}@{x}}	`KelvinBei(n, xsqrt(2)) = sum((- 1)^(n + k) BesselJ(n + 2k + 1, x)BesselI(2*k + 1, x), k = - infinity..infinity)`	`KelvinBei[n, xSqrt[2]] == Sum[(- 1)^(n + k) BesselJ[n + 2k + 1, x]BesselI[2*k + 1, x], {k, - Infinity, Infinity}, GenerateConditions->None]`	Failure	Aborted	Successful [Tested: 9]	Skipped - Because timed out
10.68#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{\nu}@{x} = (\Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x})^{\ifrac{1}{2}}}	`Error`	`Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2))^(Divide[1,2])`	Missing Macro Error	Successful	-	Successful [Tested: 30]
10.68#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{\nu}@{x} = (\Kelvinker{\nu}^{2}@@{x}+\Kelvinkei{\nu}^{2}@@{x})^{\ifrac{1}{2}}}	`Error`	`Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((KelvinKer[\[Nu], x])^(2)+ (KelvinKei[\[Nu], x])^(2))^(Divide[1,2])`	Missing Macro Error	Successful	-	Successful [Tested: 30]
10.68#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodM{-n}@{x} = \HankelmodM{n}@{x}}	`Error`	`Sqrt[KelvinBer[- n, x]^2 + KelvinBei[- n, x]^2] == Sqrt[KelvinBer[n, x]^2 + KelvinBei[n, x]^2]`	Missing Macro Error	Failure	-	Successful [Tested: 9]
10.68#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HankelmodderivN{-\nu}@{x} = \HankelmodderivN{\nu}@{x}}	`Error`	`Sqrt[KelvinKer[- \[Nu], x]^2 + KelvinKei[- \[Nu], x]^2] == Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]`	Missing Macro Error	Failure	-	Successful [Tested: 30]
10.71.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x^{1+\nu}f_{\nu}\diff{x} = -\frac{x^{1+\nu}}{\sqrt{2}}(f_{\nu+1}-g_{\nu+1})}	`int((x)^(1 + nu)* f[nu], x) = -((x)^(1 + nu))/(sqrt(2))*(f[nu + 1]- g[nu + 1])`	`Integrate[(x)^(1 + \[Nu])* Subscript[f, \[Nu]], x, GenerateConditions->None] == -Divide[(x)^(1 + \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]+ 1]- Subscript[g, \[Nu]+ 1])`	Failure	Failure	Failed [300 / 300] `300/300]: [[.9346151411+.5776724966I <- {nu = 1/23^(1/2)+1/2I, x = 3/2, f[nu] = 1/23^(1/2)+1/2I, f[1+nu] = 1/23^(1/2)+1/2I, g[1+nu] = 1/23^(1/2)+1/2I}` `3.061934630+.4518721345I <- {nu = 1/23^(1/2)+1/2I, x = 3/2, f[nu] = 1/23^(1/2)+1/2I, f[1+nu] = 1/23^(1/2)+1/2I, g[1+nu] = -1/2+1/2I3^(1/2)}`	Failed [300 / 300] `{Complex[0.9346151408625077, 0.5776724967688012] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[3.061934629891139, 0.45187213490403344] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.71.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x^{1-\nu}f_{\nu}\diff{x} = \frac{x^{1-\nu}}{\sqrt{2}}(f_{\nu-1}-g_{\nu-1})}	`int((x)^(1 - nu)* f[nu], x) = ((x)^(1 - nu))/(sqrt(2))*(f[nu - 1]- g[nu - 1])`	`Integrate[(x)^(1 - \[Nu])* Subscript[f, \[Nu]], x, GenerateConditions->None] == Divide[(x)^(1 - \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]- 1]- Subscript[g, \[Nu]- 1])`	Failure	Failure	Failed [300 / 300] `300/300]: [[.9470105611+.8580421171I <- {nu = 1/23^(1/2)+1/2I, x = 3/2, f[nu] = 1/23^(1/2)+1/2I, f[nu-1] = 1/23^(1/2)+1/2I, g[nu-1] = 1/23^(1/2)+1/2I}` `.30703090e-2+1.331056152I <- {nu = 1/23^(1/2)+1/2I, x = 3/2, f[nu] = 1/23^(1/2)+1/2I, f[nu-1] = 1/23^(1/2)+1/2I, g[nu-1] = -1/2+1/2I3^(1/2)}`	Failed [300 / 300] `{Complex[0.9470105613079453, 0.8580421172974921] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}` `Complex[0.0030703089818392426, 1.3310561520338196] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[-1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}`
10.71.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int xf_{\nu}g_{\nu}\diff{x} = \tfrac{1}{4}x^{2}\left(2f_{\nu}g_{\nu}-f_{\nu-1}g_{\nu+1}-f_{\nu+1}g_{\nu-1}\right)}	`int(xf[nu]g[nu], x) = (1)/(4)(x)^(2)(2f[nu]g[nu]- f[nu - 1]g[nu + 1]- f[nu + 1]g[nu - 1])`	`Integrate[xSubscript[f, \[Nu]]Subscript[g, \[Nu]], x, GenerateConditions->None] == Divide[1,4](x)^(2)(2Subscript[f, \[Nu]]Subscript[g, \[Nu]]- Subscript[f, \[Nu]- 1]Subscript[g, \[Nu]+ 1]- Subscript[f, \[Nu]+ 1]Subscript[g, \[Nu]- 1])`	Failure	Failure	Failed [270 / 300] `270/300]: [[.5625000004+.9742785795I <- {nu = 1/23^(1/2)+1/2I, x = 3/2, f[nu] = 1/23^(1/2)+1/2I, f[1+nu] = 1/23^(1/2)+1/2I, f[nu-1] = 1/23^(1/2)+1/2I, g[nu] = 1/23^(1/2)+1/2I, g[1+nu] = 1/23^(1/2)+1/2I, g[nu-1] = 1/23^(1/2)+1/2I}` `-.2058892896+.7683892900I <- {nu = 1/23^(1/2)+1/2I, x = 3/2, f[nu] = 1/23^(1/2)+1/2I, f[1+nu] = 1/23^(1/2)+1/2I, f[nu-1] = 1/23^(1/2)+1/2I, g[nu] = 1/23^(1/2)+1/2I, g[1+nu] = 1/23^(1/2)+1/2I, g[nu-1] = -1/2+1/2I3^(1/2)}`	Skipped - Because timed out
10.71.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x(f_{\nu}^{2}-g_{\nu}^{2})\diff{x} = \tfrac{1}{2}x^{2}\left(f_{\nu}^{2}-f_{\nu-1}f_{\nu+1}-g_{\nu}^{2}+g_{\nu-1}g_{\nu+1}\right)}	`int(x(f(f[nu])^(2)- g(g[nu])^(2)), x) = (f(f[nu])^(2)- f[nu - 1]f[nu + 1]- g(g[nu])^(2)+ g[nu - 1]*g[nu + 1])`	`Integrate[x(f(Subscript[f, \[Nu]])^(2)- g(Subscript[g, \[Nu]])^(2)), x, GenerateConditions->None] == (f(Subscript[f, \[Nu]])^(2)- Subscript[f, \[Nu]- 1]Subscript[f, \[Nu]+ 1]- g(Subscript[g, \[Nu]])^(2)+ Subscript[g, \[Nu]- 1]*Subscript[g, \[Nu]+ 1])`	Failure	Failure	Error	Error
10.71#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x\HankelmodM{\nu}^{2}@{x}\diff{x} = x(\Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x})}	`Error`	`Integrate[x(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x(KelvinBer[\[Nu], x]D[KelvinBei[\[Nu], x], {x, 1}]- D[KelvinBer[\[Nu], x], {x, 1}]KelvinBei[\[Nu], x])`	Missing Macro Error	Successful	-	Successful [Tested: 30]
10.71#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int x\HankelmodderivN{\nu}^{2}@{x}\diff{x} = x(\Kelvinker{\nu}@@{x}\Kelvinkei{\nu}'@@{x}-\Kelvinker{\nu}'@@{x}\Kelvinkei{\nu}@@{x})}	`Error`	`Integrate[x(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x(KelvinKer[\[Nu], x]D[KelvinKei[\[Nu], x], {x, 1}]- D[KelvinKer[\[Nu], x], {x, 1}]KelvinKei[\[Nu], x])`	Missing Macro Error	Successful	-	Successful [Tested: 30]
10.73.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{r}\pderiv{}{r}\left(r\pderiv{V}{r}\right)+\frac{1}{r^{2}}\pderiv[2]{V}{\phi}+\pderiv[2]{V}{z} = 0}	`(1)/(r)diff((rdiff(V, r))+(1)/((r)^(2))*diff(V, [phi$(2)]), r)+ diff(V, [z$(2)]) = 0`	`Divide[1,r]D[(rD[V, r])+Divide[1,(r)^(2)]*D[V, {\[Phi], 2}], r]+ D[V, {z, 2}] == 0`	Successful	Successful	-	Successful [Tested: 300]

@@ Line 27: / Line 27: @@
 | [https://dlmf.nist.gov/10.34#Ex2 10.34#Ex2] || [[Item:Q3549|<math>\modBesselK{\nu}@{\conj{z}} = \conj{\modBesselK{\nu}@{z}}</math>]] || <code>BesselK(nu, conjugate(z)) = conjugate(BesselK(nu, z))</code> || <code>BesselK[\[Nu], Conjugate[z]] == Conjugate[BesselK[\[Nu], z]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 70]<div class="mw-collapsible-content"><code>28/70]: [[-.3322466664+.1347267497*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>.8978926857-1.555608423*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 70]<div class="mw-collapsible-content"><code>{Complex[-0.332246666369582, 0.13472674975137633] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.23222824698313052, -0.12812607679285354] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.35.E1 10.35.E1] || [[Item:Q3550|<math>e^{\frac{1}{2}z(t+t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\modBesselI{m}@{z}</math>]] || <code>exp((1)/(2)*z*(t + (t)^(- 1))) = sum((t)^(m)* BesselI(m, z), m = - infinity..infinity)</code> || <code>Exp[Divide[1,2]*z*(t + (t)^(- 1))] == Sum[(t)^(m)* BesselI[m, z], {m, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Error || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.35.E1 10.35.E1] || [[Item:Q3550|<math>e^{\frac{1}{2}z(t+t^{-1})} = \sum_{m=-\infty}^{\infty}t^{m}\modBesselI{m}@{z}</math>]] || <code>exp((1)/(2)*z*(t + (t)^(- 1))) = sum((t)^(m)* BesselI(m, z), m = - infinity..infinity)</code> || <code>Exp[Divide[1,2]*z*(t + (t)^(- 1))] == Sum[(t)^(m)* BesselI[m, z], {m, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.35.E2 10.35.E2] || [[Item:Q3551|<math>e^{z\cos@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\modBesselI{k}@{z}\cos@{k\theta}</math>]] || <code>exp(z*cos(theta)) = BesselI(0, z)+ 2*sum(BesselI(k, z)*cos(k*theta), k = 1..infinity)</code> || <code>Exp[z*Cos[\[Theta]]] == BesselI[0, z]+ 2*Sum[BesselI[k, z]*Cos[k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Successful || Skipped - Because timed out || Successful [Tested: 70]
 |-
-| [https://dlmf.nist.gov/10.35.E3 10.35.E3] || [[Item:Q3552|<math>e^{z\sin@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=0}^{\infty}(-1)^{k}\modBesselI{2k+1}@{z}\sin@{(2k+1)\theta}+2\sum_{k=1}^{\infty}(-1)^{k}\modBesselI{2k}@{z}\cos@{2k\theta}</math>]] || <code>exp(z*sin(theta)) = BesselI(0, z)+ 2*sum((- 1)^(k)* BesselI(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity)+ 2*sum((- 1)^(k)* BesselI(2*k, z)*cos(2*k*theta), k = 1..infinity)</code> || <code>Exp[z*Sin[\[Theta]]] == BesselI[0, z]+ 2*Sum[(- 1)^(k)* BesselI[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]+ 2*Sum[(- 1)^(k)* BesselI[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.35.E3 10.35.E3] || [[Item:Q3552|<math>e^{z\sin@@{\theta}} = \modBesselI{0}@{z}+2\sum_{k=0}^{\infty}(-1)^{k}\modBesselI{2k+1}@{z}\sin@{(2k+1)\theta}+2\sum_{k=1}^{\infty}(-1)^{k}\modBesselI{2k}@{z}\cos@{2k\theta}</math>]] || <code>exp(z*sin(theta)) = BesselI(0, z)+ 2*sum((- 1)^(k)* BesselI(2*k + 1, z)*sin((2*k + 1)* theta), k = 0..infinity)+ 2*sum((- 1)^(k)* BesselI(2*k, z)*cos(2*k*theta), k = 1..infinity)</code> || <code>Exp[z*Sin[\[Theta]]] == BesselI[0, z]+ 2*Sum[(- 1)^(k)* BesselI[2*k + 1, z]*Sin[(2*k + 1)* \[Theta]], {k, 0, Infinity}, GenerateConditions->None]+ 2*Sum[(- 1)^(k)* BesselI[2*k, z]*Cos[2*k*\[Theta]], {k, 1, Infinity}, GenerateConditions->None]</code> || Aborted || Failure || Manual Skip! || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.35.E4 10.35.E4] || [[Item:Q3553|<math>1 = \modBesselI{0}@{z}-2\modBesselI{2}@{z}+2\modBesselI{4}@{z}-2\modBesselI{6}@{z}+\dotsb</math>]] || <code>1 = BesselI(0, z)- 2*BesselI(2, z)+ 2*BesselI(4, z)- 2*BesselI(6, z)+ ..</code> || <code>1 == BesselI[0, z]- 2*BesselI[2, z]+ 2*BesselI[4, z]- 2*BesselI[6, z]+ \[Ellipsis]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[-9.440290591519046*^-8, -1.7199789187696823*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-9.924736610669727*^-8, -1.6360842739013975*^-7], Times[-1.0, …]] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 72: / Line 72: @@
 |-
 | [https://dlmf.nist.gov/10.40.E10 10.40.E10] || [[Item:Q3588|<math>\modBesselK{\nu}@{z} = \left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}(\nu,z)\right)</math>]] || <code>BesselK(nu, z) = ((Pi)/(2*z))^((1)/(2))* exp(- z)*(sum((a[k]*(nu))/((z)^(k)), k = 0..ell - 1)+ R[ell]*(nu , z))</code> || <code>BesselK[\[Nu], z] == (Divide[Pi,2*z])^(Divide[1,2])* Exp[- z]*(Sum[Divide[Subscript[a, k]*(\[Nu]),(z)^(k)], {k, 0, \[ScriptL]- 1}, GenerateConditions->None]+ Subscript[R, \[ScriptL]]*(\[Nu], z))</code> || Failure || Failure || Error || Error
+|-
+| [https://dlmf.nist.gov/10.40.E13 10.40.E13] || [[Item:Q3591|<math>R_{\ell}(\nu,z) = (-1)^{\ell}2\cos@{\nu\pi}\*\left(\sum_{k=0}^{m-1}\frac{a_{k}(\nu)}{z^{k}}\scterminant{\ell-k}@{2z}+R_{m,\ell}(\nu,z)\right)</math>]] || <code>R[ell]*(nu , z) = (- 1)^(ell)* 2*cos(nu*Pi)*(sum((a[k]*(nu))/((z)^(k))*(exp(2*z)/(2*Pi))*GAMMA(ell - k)*GAMMA(1-ell - k,2*z), k = 0..m - 1)+ R[m , ell]*(nu , z))</code> || <code>Error</code> || Error || Missing Macro Error || - || -
 |-
 | [https://dlmf.nist.gov/10.41.E8 10.41.E8] || [[Item:Q3600|<math>p = (1+z^{2})^{-\frac{1}{2}}</math>]] || <code>p = (1 + (z)^(2))^(-(1)/(2))</code> || <code>p == (1 + (z)^(2))^(-Divide[1,2])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
@@ Line 91: / Line 93: @@
 | [https://dlmf.nist.gov/10.43.E4 10.43.E4] || [[Item:Q3618|<math>\frac{1}{2}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{\digamma@{k+1}-\digamma@{1}}{k!}(\tfrac{1}{2}x)^{k}\modBesselI{k}@{x} = \frac{2}{x}\sum_{k=0}^{\infty}(-1)^{k}(2k+3)(\digamma@{k+2}-\digamma@{1})\modBesselI{2k+3}@{x}</math>]] || <code>(1)/(2)*sum((- 1)^(k - 1)*(Psi(k + 1)- Psi(1))/(factorial(k))*((1)/(2)*x)^(k)* BesselI(k, x), k = 1..infinity) = (2)/(x)*sum((- 1)^(k)*(2*k + 3)*(Psi(k + 2)- Psi(1))* BesselI(2*k + 3, x), k = 0..infinity)</code> || <code>Divide[1,2]*Sum[(- 1)^(k - 1)*Divide[PolyGamma[k + 1]- PolyGamma[1],(k)!]*(Divide[1,2]*x)^(k)* BesselI[k, x], {k, 1, Infinity}, GenerateConditions->None] == Divide[2,x]*Sum[(- 1)^(k)*(2*k + 3)*(PolyGamma[k + 2]- PolyGamma[1])* BesselI[2*k + 3, x], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[Times[0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.75, k], BesselI[k, 1.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-1.3333333333333333, NSum[Times[Power[-1, k], Plus[3, Times[2, k]], BesselI[Plus[3, Times[2, k]], 1.5], Plus[EulerGamma, PolyGamma[0, Plus[2, k]]]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5]}</code><br><code>Plus[Times[0.5, NSum[Times[Power[-1, Plus[-1, k]], Power[0.25, k], BesselI[k, 0.5], Power[Factorial[k], -1], Plus[EulerGamma, PolyGamma[0, Plus[1, k]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], Times[-4.0, NSum[Times[Power[-1, k], Plus[3, Times[2, k]], BesselI[Plus[3, Times[2, k]], 0.5], Plus[EulerGamma, PolyGamma[0, Plus[2, k]]]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.43.E5 10.43.E5] || [[Item:Q3619|<math>\int_{x}^{\infty}\frac{\modBesselK{0}@{t}}{t}\diff{t} = \frac{1}{2}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi^{2}}{24}-\sum_{k=1}^{\infty}\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}</math>]] || <code>int((BesselK(0, t))/(t), t = x..infinity) = (1)/(2)*(ln((1)/(2)*x)+ gamma)^(2)+((Pi)^(2))/(24)- sum((Psi(k + 1)+(1)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity)</code> || <code>Integrate[Divide[BesselK[0, t],t], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[Divide[1,2]*x]+ EulerGamma)^(2)+Divide[(Pi)^(2),24]- Sum[(PolyGamma[k + 1]+Divide[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 3] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.43.E5 10.43.E5] || [[Item:Q3619|<math>\int_{x}^{\infty}\frac{\modBesselK{0}@{t}}{t}\diff{t} = \frac{1}{2}\left(\ln@{\tfrac{1}{2}x}+\EulerConstant\right)^{2}+\frac{\pi^{2}}{24}-\sum_{k=1}^{\infty}\left(\digamma@{k+1}+\frac{1}{2k}-\ln@{\tfrac{1}{2}x}\right)\frac{(\tfrac{1}{2}x)^{2k}}{2k(k!)^{2}}</math>]] || <code>int((BesselK(0, t))/(t), t = x..infinity) = (1)/(2)*(ln((1)/(2)*x)+ gamma)^(2)+((Pi)^(2))/(24)- sum((Psi(k + 1)+(1)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(factorial(k))^(2)), k = 1..infinity)</code> || <code>Integrate[Divide[BesselK[0, t],t], {t, x, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[Divide[1,2]*x]+ EulerGamma)^(2)+Divide[(Pi)^(2),24]- Sum[(PolyGamma[k + 1]+Divide[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((k)!)^(2)], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 3] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.43.E6 10.43.E6] || [[Item:Q3620|<math>\int_{0}^{x}e^{-t}\modBesselI{n}@{t}\diff{t} = xe^{-x}(\modBesselI{0}@{x}+\modBesselI{1}@{x})+n(e^{-x}\modBesselI{0}@{x}-1)+2e^{-x}\sum_{k=1}^{n-1}(n-k)\modBesselI{k}@{x}</math>]] || <code>int(exp(- t)*BesselI(n, t), t = 0..x) = x*exp(- x)*(BesselI(0, x)+ BesselI(1, x))+ n*(exp(- x)*BesselI(0, x)- 1)+ 2*exp(- x)*sum((n - k)* BesselI(k, x), k = 1..n - 1)</code> || <code>Integrate[Exp[- t]*BesselI[n, t], {t, 0, x}, GenerateConditions->None] == x*Exp[- x]*(BesselI[0, x]+ BesselI[1, x])+ n*(Exp[- x]*BesselI[0, x]- 1)+ 2*Exp[- x]*Sum[(n - k)* BesselI[k, x], {k, 1, n - 1}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><code>{Plus[1.0269197346695518, Times[-0.44626032029685964, Plus[-4.940169569318671, Times[3.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[1.5, []], Times[Plus[-2, Times[-2, ], Times[-1, 1.5]], [Plus[1, ]]], Times[Plus[2, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[1.5, [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], BesselI[0, 1.5]], Equal[[2], Plus[BesselI[0, 1.5], BesselI[1, 1.5]]]}]][3.0]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], 1.5, []], Times[-1, Plus[2, ], Plus[Times[2, ], 1.5], [Plus[1, ]]], Times[, Plus[4, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[, 1.5, [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], BesselI[1, 1.5]], Equal[[3], Plus[Times[2, Power[1.5, -1], Plus[Times[1.5, BesselI[0, 1.5]], Times[-2, BesselI[1, 1.5]]]], BesselI[1, 1.5]]]}]][3.0]]]]], {Rule[n, 3], Rule[x, 1.5]}</code><br><code>Plus[0.6643873281588137, Times[-1.2130613194252668, Plus[-3.19045011222397, Times[3.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[0.5, []], Times[Plus[-2, Times[-2, ], Times[-1, 0.5]], [Plus[1, ]]], Times[Plus[2, Times[2, ], Times[-1, 0.5]], [Plus[2, ]]], Times[0.5, [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], BesselI[0, 0.5]], Equal[[2], Plus[BesselI[0, 0.5], BesselI[1, 0.5]]]}]][3.0]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], 0.5, []], Times[-1, Plus[2, ], Plus[Times[2, ], 0.5], [Plus[1, ]]], Times[, Plus[4, Times[2, ], Times[-1, 0.5]], [Plus[2, ]]], Times[, 0.5, [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], BesselI[1, 0.5]], Equal[[3], Plus[Times[2, Power[0.5, -1], Plus[Times[0.5, BesselI[0, 0.5]], Times[-2, BesselI[1, 0.5]]]], BesselI[1, 0.5]]]}]][3.0]]]]], {Rule[n, 3], Rule[x, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E6 10.43.E6] || [[Item:Q3620|<math>\int_{0}^{x}e^{-t}\modBesselI{n}@{t}\diff{t} = xe^{-x}(\modBesselI{0}@{x}+\modBesselI{1}@{x})+n(e^{-x}\modBesselI{0}@{x}-1)+2e^{-x}\sum_{k=1}^{n-1}(n-k)\modBesselI{k}@{x}</math>]] || <code>int(exp(- t)*BesselI(n, t), t = 0..x) = x*exp(- x)*(BesselI(0, x)+ BesselI(1, x))+ n*(exp(- x)*BesselI(0, x)- 1)+ 2*exp(- x)*sum((n - k)* BesselI(k, x), k = 1..n - 1)</code> || <code>Integrate[Exp[- t]*BesselI[n, t], {t, 0, x}, GenerateConditions->None] == x*Exp[- x]*(BesselI[0, x]+ BesselI[1, x])+ n*(Exp[- x]*BesselI[0, x]- 1)+ 2*Exp[- x]*Sum[(n - k)* BesselI[k, x], {k, 1, n - 1}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 3] || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><code>{Plus[1.0269197346695518, Times[-0.44626032029685964, Plus[-4.940169569318671, Times[3.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[1.5, []], Times[Plus[-2, Times[-2, ], Times[-1, 1.5]], [Plus[1, ]]], Times[Plus[2, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[1.5, [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], BesselI[0, 1.5]], Equal[[2], Plus[BesselI[0, 1.5], BesselI[1, 1.5]]]}]][3.0]], Times[-1.0, DifferenceRoot[Function[{, }, {Equal[Plus[Times[Plus[2, ], 1.5, []], Times[-1, Plus[2, ], Plus[Times[2, ], 1.5], [Plus[1, ]]], Times[, Plus[4, Times[2, ], Times[-1, 1.5]], [Plus[2, ]]], Times[, 1.5, [Plus[3, ]]]], 0], Equal[[1], 0], Equal[[2], BesselI[1, 1.5]], Equal[[3], Plus[Times[2, Power[1.5, -1], Plus[Times[1.5, BesselI[0, 1.5]], Times[-2, BesselI[1, 1.5]]]], BesselI[1, 1.5]]]}]][3.0]]]]], {Rule[n, 3], Rule[x, 1.5]}</code><br><code>Plus[0.6643873281588137, Times[-1.2130613194252668, Plus[-3.19045011222397, Times[3.0, DifferenceRoot[Func</div></div>
 |-
 | [https://dlmf.nist.gov/10.43.E7 10.43.E7] || [[Item:Q3621|<math>\int_{0}^{x}e^{+ t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}-\modBesselI{\nu+1}@{x})</math>]] || <code>int(exp(+ t)*(t)^(nu)* BesselI(nu, t), t = 0..x) = (exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselI(nu, x)- BesselI(nu + 1, x))</code> || <code>Integrate[Exp[+ t]*(t)^\[Nu]* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]+ 1, x])</code> || Failure || Successful || Successful [Tested: 15] || Successful [Tested: 15]
@@ Line 99: / Line 101: @@
 | [https://dlmf.nist.gov/10.43.E7 10.43.E7] || [[Item:Q3621|<math>\int_{0}^{x}e^{- t}t^{\nu}\modBesselI{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselI{\nu}@{x}+\modBesselI{\nu+1}@{x})</math>]] || <code>int(exp(- t)*(t)^(nu)* BesselI(nu, t), t = 0..x) = (exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselI(nu, x)+ BesselI(nu + 1, x))</code> || <code>Integrate[Exp[- t]*(t)^\[Nu]* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]+ 1, x])</code> || Failure || Successful || Skipped - Because timed out || Successful [Tested: 15]
 |-
-| [https://dlmf.nist.gov/10.43.E8 10.43.E8] || [[Item:Q3622|<math>\int_{0}^{x}e^{+ t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{+ x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}-\modBesselI{\nu-1}@{x})-\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}</math>]] || <code>int(exp(+ t)*(t)^(- nu)* BesselI(nu, t), t = 0..x) = -(exp(+ x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)- BesselI(nu - 1, x))-((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu))</code> || <code>Integrate[Exp[+ t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[+ x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]- 1, x])-Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]]</code> || Failure || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 12]<div class="mw-collapsible-content"><code>{0.39894228040143315 <- {Rule[x, 1.5], Rule[ν, 1.5]}</code><br><code>0.39894228040143254 <- {Rule[x, 0.5], Rule[ν, 1.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E8 10.43.E8] || [[Item:Q3622|<math>\int_{0}^{x}e^{+ t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{+ x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}-\modBesselI{\nu-1}@{x})-\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}</math>]] || <code>int(exp(+ t)*(t)^(- nu)* BesselI(nu, t), t = 0..x) = -(exp(+ x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)- BesselI(nu - 1, x))-((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu))</code> || <code>Integrate[Exp[+ t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[+ x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]- BesselI[\[Nu]- 1, x])-Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]]</code> || Failure || Successful || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 12]<div class="mw-collapsible-content"><code>{0.39894228040143315 <- {Rule[x, 1.5], Rule[ν, 1.5]}</code><br><code>0.39894228040143254 <- {Rule[x, 0.5], Rule[ν, 1.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.43.E8 10.43.E8] || [[Item:Q3622|<math>\int_{0}^{x}e^{- t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{- x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}+\modBesselI{\nu-1}@{x})+\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}</math>]] || <code>int(exp(- t)*(t)^(- nu)* BesselI(nu, t), t = 0..x) = -(exp(- x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)+ BesselI(nu - 1, x))+((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu))</code> || <code>Integrate[Exp[- t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[- x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]- 1, x])+Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]]</code> || Failure || Successful || - || Successful [Tested: 12]
+| [https://dlmf.nist.gov/10.43.E8 10.43.E8] || [[Item:Q3622|<math>\int_{0}^{x}e^{- t}t^{-\nu}\modBesselI{\nu}@{t}\diff{t} = -\frac{e^{- x}x^{-\nu+1}}{2\nu-1}(\modBesselI{\nu}@{x}+\modBesselI{\nu-1}@{x})+\frac{2^{-\nu+1}}{(2\nu-1)\EulerGamma@{\nu}}</math>]] || <code>int(exp(- t)*(t)^(- nu)* BesselI(nu, t), t = 0..x) = -(exp(- x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselI(nu, x)+ BesselI(nu - 1, x))+((2)^(- nu + 1))/((2*nu - 1)* GAMMA(nu))</code> || <code>Integrate[Exp[- t]*(t)^(- \[Nu])* BesselI[\[Nu], t], {t, 0, x}, GenerateConditions->None] == -Divide[Exp[- x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselI[\[Nu], x]+ BesselI[\[Nu]- 1, x])+Divide[(2)^(- \[Nu]+ 1),(2*\[Nu]- 1)* Gamma[\[Nu]]]</code> || Failure || Successful || Manual Skip! || Successful [Tested: 12]
 |-
-| [https://dlmf.nist.gov/10.43.E9 10.43.E9] || [[Item:Q3623|<math>\int_{0}^{x}e^{+ t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}+\modBesselK{\nu+1}@{x})-\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}</math>]] || <code>int(exp(+ t)*(t)^(nu)* BesselK(nu, t), t = 0..x) = (exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)+ BesselK(nu + 1, x))-((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1)</code> || <code>Integrate[Exp[+ t]*(t)^\[Nu]* BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]+ 1, x])-Divide[(2)^\[Nu]* Gamma[\[Nu]+ 1],2*\[Nu]+ 1]</code> || Failure || Error || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 15]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 1.5]}</code><br><code>DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E9 10.43.E9] || [[Item:Q3623|<math>\int_{0}^{x}e^{+ t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{+ x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}+\modBesselK{\nu+1}@{x})-\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}</math>]] || <code>int(exp(+ t)*(t)^(nu)* BesselK(nu, t), t = 0..x) = (exp(+ x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)+ BesselK(nu + 1, x))-((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1)</code> || <code>Integrate[Exp[+ t]*(t)^\[Nu]* BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[+ x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]+ 1, x])-Divide[(2)^\[Nu]* Gamma[\[Nu]+ 1],2*\[Nu]+ 1]</code> || Failure || Aborted || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 15]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 1.5]}</code><br><code>DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.43.E9 10.43.E9] || [[Item:Q3623|<math>\int_{0}^{x}e^{- t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}-\modBesselK{\nu+1}@{x})+\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}</math>]] || <code>int(exp(- t)*(t)^(nu)* BesselK(nu, t), t = 0..x) = (exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)- BesselK(nu + 1, x))+((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1)</code> || <code>Integrate[Exp[- t]*(t)^\[Nu]* BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]- BesselK[\[Nu]+ 1, x])+Divide[(2)^\[Nu]* Gamma[\[Nu]+ 1],2*\[Nu]+ 1]</code> || Failure || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 15]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 2]}</code><br><code>DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E9 10.43.E9] || [[Item:Q3623|<math>\int_{0}^{x}e^{- t}t^{\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{- x}x^{\nu+1}}{2\nu+1}(\modBesselK{\nu}@{x}-\modBesselK{\nu+1}@{x})+\frac{2^{\nu}\EulerGamma@{\nu+1}}{2\nu+1}</math>]] || <code>int(exp(- t)*(t)^(nu)* BesselK(nu, t), t = 0..x) = (exp(- x)*(x)^(nu + 1))/(2*nu + 1)*(BesselK(nu, x)- BesselK(nu + 1, x))+((2)^(nu)* GAMMA(nu + 1))/(2*nu + 1)</code> || <code>Integrate[Exp[- t]*(t)^\[Nu]* BesselK[\[Nu], t], {t, 0, x}, GenerateConditions->None] == Divide[Exp[- x]*(x)^(\[Nu]+ 1),2*\[Nu]+ 1]*(BesselK[\[Nu], x]- BesselK[\[Nu]+ 1, x])+Divide[(2)^\[Nu]* Gamma[\[Nu]+ 1],2*\[Nu]+ 1]</code> || Failure || Successful || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 15]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[x, 1.5], Rule[ν, 2]}</code><br><code>DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.43.E10 10.43.E10] || [[Item:Q3624|<math>\int_{x}^{\infty}e^{t}t^{-\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{x}x^{-\nu+1}}{2\nu-1}(\modBesselK{\nu}@{x}+\modBesselK{\nu-1}@{x})</math>]] || <code>int(exp(t)*(t)^(- nu)* BesselK(nu, t), t = x..infinity) = (exp(x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselK(nu, x)+ BesselK(nu - 1, x))</code> || <code>Integrate[Exp[t]*(t)^(- \[Nu])* BesselK[\[Nu], t], {t, x, Infinity}, GenerateConditions->None] == Divide[Exp[x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]- 1, x])</code> || Failure || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 9]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[x, 1.5], Rule[ν, 2]}</code><br><code>DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E10 10.43.E10] || [[Item:Q3624|<math>\int_{x}^{\infty}e^{t}t^{-\nu}\modBesselK{\nu}@{t}\diff{t} = \frac{e^{x}x^{-\nu+1}}{2\nu-1}(\modBesselK{\nu}@{x}+\modBesselK{\nu-1}@{x})</math>]] || <code>int(exp(t)*(t)^(- nu)* BesselK(nu, t), t = x..infinity) = (exp(x)*(x)^(- nu + 1))/(2*nu - 1)*(BesselK(nu, x)+ BesselK(nu - 1, x))</code> || <code>Integrate[Exp[t]*(t)^(- \[Nu])* BesselK[\[Nu], t], {t, x, Infinity}, GenerateConditions->None] == Divide[Exp[x]*(x)^(- \[Nu]+ 1),2*\[Nu]- 1]*(BesselK[\[Nu], x]+ BesselK[\[Nu]- 1, x])</code> || Failure || Successful || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 9]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[x, 1.5], Rule[ν, 2]}</code><br><code>DirectedInfinity[] <- {Rule[x, 0.5], Rule[ν, 2]}</code><br></div></div>
 |-
 | [https://dlmf.nist.gov/10.43.E18 10.43.E18] || [[Item:Q3632|<math>\int_{0}^{\infty}\modBesselK{\nu}@{t}\diff{t} = \tfrac{1}{2}\pi\sec@{\tfrac{1}{2}\pi\nu}</math>]] || <code>int(BesselK(nu, t), t = 0..infinity) = (1)/(2)*Pi*sec((1)/(2)*Pi*nu)</code> || <code>Integrate[BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*Sec[Divide[1,2]*Pi*\[Nu]]</code> || Successful || Successful || - || Successful [Tested: 6]
@@ Line 113: / Line 115: @@
 | [https://dlmf.nist.gov/10.43.E19 10.43.E19] || [[Item:Q3633|<math>\int_{0}^{\infty}t^{\mu-1}\modBesselK{\nu}@{t}\diff{t} = 2^{\mu-2}\EulerGamma@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}\EulerGamma@{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu}</math>]] || <code>int((t)^(mu - 1)* BesselK(nu, t), t = 0..infinity) = (2)^(mu - 2)* GAMMA((1)/(2)*mu -(1)/(2)*nu)*GAMMA((1)/(2)*mu +(1)/(2)*nu)</code> || <code>Integrate[(t)^(\[Mu]- 1)* BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == (2)^(\[Mu]- 2)* Gamma[Divide[1,2]*\[Mu]-Divide[1,2]*\[Nu]]*Gamma[Divide[1,2]*\[Mu]+Divide[1,2]*\[Nu]]</code> || Successful || Successful || - || Successful [Tested: 18]
 |-
-| [https://dlmf.nist.gov/10.43.E20 10.43.E20] || [[Item:Q3634|<math>\int_{0}^{\infty}\cos@{at}\modBesselK{0}@{t}\diff{t} = \frac{\pi}{2(1+a^{2})^{\frac{1}{2}}}</math>]] || <code>int(cos(a*t)*BesselK(0, t), t = 0..infinity) = (Pi)/(2*(1 + (a)^(2))^((1)/(2)))</code> || <code>Integrate[Cos[a*t]*BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2*(1 + (a)^(2))^(Divide[1,2])]</code> || Successful || Error || - || Successful [Tested: 6]
+| [https://dlmf.nist.gov/10.43.E20 10.43.E20] || [[Item:Q3634|<math>\int_{0}^{\infty}\cos@{at}\modBesselK{0}@{t}\diff{t} = \frac{\pi}{2(1+a^{2})^{\frac{1}{2}}}</math>]] || <code>int(cos(a*t)*BesselK(0, t), t = 0..infinity) = (Pi)/(2*(1 + (a)^(2))^((1)/(2)))</code> || <code>Integrate[Cos[a*t]*BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Pi,2*(1 + (a)^(2))^(Divide[1,2])]</code> || Successful || Aborted || - || Successful [Tested: 6]
 |-
 | [https://dlmf.nist.gov/10.43.E21 10.43.E21] || [[Item:Q3635|<math>\int_{0}^{\infty}\sin@{at}\modBesselK{0}@{t}\diff{t} = \frac{\asinh@@{a}}{(1+a^{2})^{\frac{1}{2}}}</math>]] || <code>int(sin(a*t)*BesselK(0, t), t = 0..infinity) = (arcsinh(a))/((1 + (a)^(2))^((1)/(2)))</code> || <code>Integrate[Sin[a*t]*BesselK[0, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[ArcSinh[a],(1 + (a)^(2))^(Divide[1,2])]</code> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 6]
 |-
-| [https://dlmf.nist.gov/10.43.E24 10.43.E24] || [[Item:Q3638|<math>\int_{0}^{\infty}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselI{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}</math>]] || <code>int(BesselI(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(2*p)*exp(((b)^(2))/(8*(p)^(2)))*BesselI((1)/(2)*nu, ((b)^(2))/(8*(p)^(2)))</code> || <code>Integrate[BesselI[\[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[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [228 / 300]<div class="mw-collapsible-content"><code>228/300]: [[-.7585567167+3.675115279*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I}</code><br><code>-.9489546609+2.381017603*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = -1/2*3^(1/2)-1/2*I}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [152 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.19039794459564638, -1.294097675814569] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[2.992047945390181, -4.249025046528451] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E23 10.43.E23] || [[Item:Q3637|<math>\int_{0}^{\infty}t^{\nu+1}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp@{\frac{b^{2}}{4p^{2}}}</math>]] || <code>int((t)^(nu + 1)* BesselI(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = ((b)^(nu))/((2*(p)^(2))^(nu + 1))*exp(((b)^(2))/(4*(p)^(2)))</code> || <code>Integrate[(t)^(\[Nu]+ 1)* BesselI[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[(b)^\[Nu],(2*(p)^(2))^(\[Nu]+ 1)]*Exp[Divide[(b)^(2),4*(p)^(2)]]</code> || Error || Aborted || - || Skip - No test values generated
+|-
+| [https://dlmf.nist.gov/10.43.E24 10.43.E24] || [[Item:Q3638|<math>\int_{0}^{\infty}\modBesselI{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2p}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselI{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}</math>]] || <code>int(BesselI(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(2*p)*exp(((b)^(2))/(8*(p)^(2)))*BesselI((1)/(2)*nu, ((b)^(2))/(8*(p)^(2)))</code> || <code>Integrate[BesselI[\[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[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [228 / 300]<div class="mw-collapsible-content"><code>228/300]: [[-.7585567167+3.675115279*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I}</code><br><code>-.9489546609+2.381017603*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = -1/2*3^(1/2)-1/2*I}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [152 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.19039794459564638, -1.294097675814569] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[2.992047945390181, -4.249025046528451] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.43.E25 10.43.E25] || [[Item:Q3639|<math>\int_{0}^{\infty}\modBesselK{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{4p}\sec@{\tfrac{1}{2}\pi\nu}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselK{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}</math>]] || <code>int(BesselK(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(4*p)*sec((1)/(2)*Pi*nu)*exp(((b)^(2))/(8*(p)^(2)))*BesselK((1)/(2)*nu, ((b)^(2))/(8*(p)^(2)))</code> || <code>Integrate[BesselK[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],4*p]*Sec[Divide[1,2]*Pi*\[Nu]]*Exp[Divide[(b)^(2),8*(p)^(2)]]*BesselK[Divide[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [144 / 288]<div class="mw-collapsible-content"><code>144/288]: [[-.4056916296-1.844454275*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I}</code><br><code>-.2830456904e-1-1.996429597*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 3/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [144 / 288]<div class="mw-collapsible-content"><code>{Complex[0.40569163152223653, 1.8444542715605226] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4232355421098407, -0.8203643961026106] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.43.E26 10.43.E26] || [[Item:Q3640|<math>\int_{0}^{\infty}\frac{\modBesselK{\mu}@{at}\BesselJ{\nu}@{bt}}{t^{\lambda}}\diff{t} = \frac{b^{\nu}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\lambda+\frac{1}{2}\mu+\frac{1}{2}}\EulerGamma@{\frac{1}{2}\nu-\frac{1}{2}\lambda-\frac{1}{2}\mu+\frac{1}{2}}}{2^{\lambda+1}a^{\nu-\lambda+1}}\*\hyperOlverF@{\frac{\nu-\lambda+\mu+1}{2}}{\frac{\nu-\lambda-\mu+1}{2}}{\nu+1}{-\frac{b^{2}}{a^{2}}}</math>]] || <code>int((BesselK(mu, a*t)*BesselJ(nu, b*t))/((t)^(lambda)), t = 0..infinity) = ((b)^(nu)* GAMMA((1)/(2)*nu -(1)/(2)*lambda +(1)/(2)*mu +(1)/(2))*GAMMA((1)/(2)*nu -(1)/(2)*lambda -(1)/(2)*mu +(1)/(2)))/((2)^(lambda + 1)* (a)^(nu - lambda + 1))* hypergeom([(nu - lambda + mu + 1)/(2), (nu - lambda - mu + 1)/(2)], [nu + 1], -((b)^(2))/((a)^(2)))/GAMMA(nu + 1)</code> || <code>Integrate[Divide[BesselK[\[Mu], a*t]*BesselJ[\[Nu], b*t],(t)^\[Lambda]], {t, 0, Infinity}, GenerateConditions->None] == Divide[(b)^\[Nu]* Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Lambda]+Divide[1,2]*\[Mu]+Divide[1,2]]*Gamma[Divide[1,2]*\[Nu]-Divide[1,2]*\[Lambda]-Divide[1,2]*\[Mu]+Divide[1,2]],(2)^(\[Lambda]+ 1)* (a)^(\[Nu]- \[Lambda]+ 1)]* Hypergeometric2F1Regularized[Divide[\[Nu]- \[Lambda]+ \[Mu]+ 1,2], Divide[\[Nu]- \[Lambda]- \[Mu]+ 1,2], \[Nu]+ 1, -Divide[(b)^(2),(a)^(2)]]</code> || Error || Aborted || - || Skip - No test values generated
+|-
+| [https://dlmf.nist.gov/10.43.E27 10.43.E27] || [[Item:Q3641|<math>\int_{0}^{\infty}t^{\mu+\nu+1}\modBesselK{\mu}@{at}\BesselJ{\nu}@{bt}\diff{t} = \frac{(2a)^{\mu}(2b)^{\nu}\EulerGamma@{\mu+\nu+1}}{(a^{2}+b^{2})^{\mu+\nu+1}}</math>]] || <code>int((t)^(mu + nu + 1)* BesselK(mu, a*t)*BesselJ(nu, b*t), t = 0..infinity) = ((2*a)^(mu)*(2*b)^(nu)* GAMMA(mu + nu + 1))/(((a)^(2)+ (b)^(2))^(mu + nu + 1))</code> || <code>Integrate[(t)^(\[Mu]+ \[Nu]+ 1)* BesselK[\[Mu], a*t]*BesselJ[\[Nu], b*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[(2*a)^\[Mu]*(2*b)^\[Nu]* Gamma[\[Mu]+ \[Nu]+ 1],((a)^(2)+ (b)^(2))^(\[Mu]+ \[Nu]+ 1)]</code> || Error || Aborted || - || Skip - No test values generated
 |-
-| [https://dlmf.nist.gov/10.43.E25 10.43.E25] || [[Item:Q3639|<math>\int_{0}^{\infty}\modBesselK{\nu}@{bt}\exp@{-p^{2}t^{2}}\diff{t} = \frac{\sqrt{\pi}}{4p}\sec@{\tfrac{1}{2}\pi\nu}\exp@{\frac{b^{2}}{8p^{2}}}\modBesselK{\frac{1}{2}\nu}@{\frac{b^{2}}{8p^{2}}}</math>]] || <code>int(BesselK(nu, b*t)*exp(- (p)^(2)* (t)^(2)), t = 0..infinity) = (sqrt(Pi))/(4*p)*sec((1)/(2)*Pi*nu)*exp(((b)^(2))/(8*(p)^(2)))*BesselK((1)/(2)*nu, ((b)^(2))/(8*(p)^(2)))</code> || <code>Integrate[BesselK[\[Nu], b*t]*Exp[- (p)^(2)* (t)^(2)], {t, 0, Infinity}, GenerateConditions->None] == Divide[Sqrt[Pi],4*p]*Sec[Divide[1,2]*Pi*\[Nu]]*Exp[Divide[(b)^(2),8*(p)^(2)]]*BesselK[Divide[1,2]*\[Nu], Divide[(b)^(2),8*(p)^(2)]]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [144 / 288]<div class="mw-collapsible-content"><code>144/288]: [[-.4056916296-1.844454275*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I}</code><br><code>-.2830456904e-1-1.996429597*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, p = 3/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [144 / 288]<div class="mw-collapsible-content"><code>{Complex[0.40569163152223653, 1.8444542715605226] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4232355421098407, -0.8203643961026106] <- {Rule[b, -1.5], Rule[p, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.43.E28 10.43.E28] || [[Item:Q3642|<math>\int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\modBesselI{\nu}@{at}\modBesselI{\nu}@{bt}\diff{t} = \frac{1}{2p^{2}}\exp@{\frac{a^{2}+b^{2}}{4p^{2}}}\modBesselI{\nu}@{\frac{ab}{2p^{2}}}</math>]] || <code>int(t*exp(- (p)^(2)* (t)^(2))*BesselI(nu, a*t)*BesselI(nu, b*t), t = 0..infinity) = (1)/(2*(p)^(2))*exp(((a)^(2)+ (b)^(2))/(4*(p)^(2)))*BesselI(nu, (a*b)/(2*(p)^(2)))</code> || <code>Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselI[\[Nu], a*t]*BesselI[\[Nu], b*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2*(p)^(2)]*Exp[Divide[(a)^(2)+ (b)^(2),4*(p)^(2)]]*BesselI[\[Nu], Divide[a*b,2*(p)^(2)]]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.43.E29 10.43.E29] || [[Item:Q3643|<math>\int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\modBesselI{0}@{at}\modBesselK{0}@{at}\diff{t} = \frac{1}{4p^{2}}\exp@{\frac{a^{2}}{2p^{2}}}\modBesselK{0}@{\frac{a^{2}}{2p^{2}}}</math>]] || <code>int(t*exp(- (p)^(2)* (t)^(2))*BesselI(0, a*t)*BesselK(0, a*t), t = 0..infinity) = (1)/(4*(p)^(2))*exp(((a)^(2))/(2*(p)^(2)))*BesselK(0, ((a)^(2))/(2*(p)^(2)))</code> || <code>Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselI[0, a*t]*BesselK[0, a*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,4*(p)^(2)]*Exp[Divide[(a)^(2),2*(p)^(2)]]*BesselK[0, Divide[(a)^(2),2*(p)^(2)]]</code> || Failure || Error || Skipped - Because timed out || Successful [Tested: 48]
+| [https://dlmf.nist.gov/10.43.E29 10.43.E29] || [[Item:Q3643|<math>\int_{0}^{\infty}t\exp@{-p^{2}t^{2}}\modBesselI{0}@{at}\modBesselK{0}@{at}\diff{t} = \frac{1}{4p^{2}}\exp@{\frac{a^{2}}{2p^{2}}}\modBesselK{0}@{\frac{a^{2}}{2p^{2}}}</math>]] || <code>int(t*exp(- (p)^(2)* (t)^(2))*BesselI(0, a*t)*BesselK(0, a*t), t = 0..infinity) = (1)/(4*(p)^(2))*exp(((a)^(2))/(2*(p)^(2)))*BesselK(0, ((a)^(2))/(2*(p)^(2)))</code> || <code>Integrate[t*Exp[- (p)^(2)* (t)^(2)]*BesselI[0, a*t]*BesselK[0, a*t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,4*(p)^(2)]*Exp[Divide[(a)^(2),2*(p)^(2)]]*BesselK[0, Divide[(a)^(2),2*(p)^(2)]]</code> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 48]
 |-
 | [https://dlmf.nist.gov/10.44#Ex1 10.44#Ex1] || [[Item:Q3649|<math>\modBesselI{\nu}@{z} = \sum_{k=0}^{\infty}\frac{z^{k}}{k!}\BesselJ{\nu+k}@{z}</math>]] || <code>BesselI(nu, z) = sum(((z)^(k))/(factorial(k))*BesselJ(nu + k, z), k = 0..infinity)</code> || <code>BesselI[\[Nu], z] == Sum[Divide[(z)^(k),(k)!]*BesselJ[\[Nu]+ k, z], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Successful || Skipped - Because timed out || Successful [Tested: 70]
@@ Line 127: / Line 137: @@
 | [https://dlmf.nist.gov/10.44#Ex2 10.44#Ex2] || [[Item:Q3650|<math>\BesselJ{\nu}@{z} = \sum_{k=0}^{\infty}(-1)^{k}\frac{z^{k}}{k!}\modBesselI{\nu+k}@{z}</math>]] || <code>BesselJ(nu, z) = sum((- 1)^(k)*((z)^(k))/(factorial(k))*BesselI(nu + k, z), k = 0..infinity)</code> || <code>BesselJ[\[Nu], z] == Sum[(- 1)^(k)*Divide[(z)^(k),(k)!]*BesselI[\[Nu]+ k, z], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Plus[Complex[0.4358908643715884, -0.07192294931339177], Times[-1.0, NSum[Times[Power[-1, k], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[1.0679098760861825, 0.09257666026367889], Times[-1.0, NSum[Times[Power[-1, k], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], BesselI[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.44.E4 10.44.E4] || [[Item:Q3652|<math>\left(\tfrac{1}{2}z\right)^{\nu} = \sum_{k=0}^{\infty}(-1)^{k}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\modBesselI{\nu+2k}@{z}</math>]] || <code>((1)/(2)*z)^(nu) = sum((- 1)^(k)*((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselI(nu + 2*k, z), k = 0..infinity)</code> || <code>(Divide[1,2]*z)^\[Nu] == Sum[(- 1)^(k)*Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselI[\[Nu]+ 2*k, z], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1]}</code><br><code>Plus[Complex[-0.2499999999999999, 0.43301270189221935], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 1]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.44.E4 10.44.E4] || [[Item:Q3652|<math>\left(\tfrac{1}{2}z\right)^{\nu} = \sum_{k=0}^{\infty}(-1)^{k}\frac{(\nu+2k)\EulerGamma@{\nu+k}}{k!}\modBesselI{\nu+2k}@{z}</math>]] || <code>((1)/(2)*z)^(nu) = sum((- 1)^(k)*((nu + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselI(nu + 2*k, z), k = 0..infinity)</code> || <code>(Divide[1,2]*z)^\[Nu] == Sum[(- 1)^(k)*Divide[(\[Nu]+ 2*k)* Gamma[\[Nu]+ k],(k)!]*BesselI[\[Nu]+ 2*k, z], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 1]}</code><br><code>Plus[Complex[-0.2499999999999999, 0.43301270189221935], Times[-1.0, NSum[Times[Power[-1, k], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Power[Factorial[k], -1], Gamma[Plus[1, k]]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, 1]}</code><br></div></div>
 |-
 | [https://dlmf.nist.gov/10.44.E5 10.44.E5] || [[Item:Q3653|<math>\modBesselK{0}@{z} = -\left(\ln@{\tfrac{1}{2}z}+\EulerConstant\right)\modBesselI{0}@{z}+2\sum_{k=1}^{\infty}\frac{\modBesselI{2k}@{z}}{k}</math>]] || <code>BesselK(0, z) = -(ln((1)/(2)*z)+ gamma)* BesselI(0, z)+ 2*sum((BesselI(2*k, z))/(k), k = 1..infinity)</code> || <code>BesselK[0, z] == -(Log[Divide[1,2]*z]+ EulerGamma)* BesselI[0, z]+ 2*Sum[Divide[BesselI[2*k, z],k], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.44.E6 10.44.E6] || [[Item:Q3654|<math>\modBesselK{n}@{z} = \frac{n!(\tfrac{1}{2}z)^{-n}}{2}\sum_{k=0}^{n-1}(-1)^{k}\frac{(\tfrac{1}{2}z)^{k}\modBesselI{k}@{z}}{k!(n-k)}+(-1)^{n-1}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\modBesselI{n}@{z}+(-1)^{n}\sum_{k=1}^{\infty}\frac{(n+2k)\modBesselI{n+2k}@{z}}{k(n+k)}</math>]] || <code>BesselK(n, z) = (factorial(n)*((1)/(2)*z)^(- n))/(2)*sum((- 1)^(k)*(((1)/(2)*z)^(k)* BesselI(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(- 1)^(n - 1)*(ln((1)/(2)*z)- Psi(n + 1))* BesselI(n, z)+(- 1)^(n)* sum(((n + 2*k)* BesselI(n + 2*k, z))/(k*(n + k)), k = 1..infinity)</code> || <code>BesselK[n, z] == Divide[(n)!*(Divide[1,2]*z)^(- n),2]*Sum[(- 1)^(k)*Divide[(Divide[1,2]*z)^(k)* BesselI[k, z],(k)!*(n - k)], {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n - 1)*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselI[n, z]+(- 1)^(n)* Sum[Divide[(n + 2*k)* BesselI[n + 2*k, z],k*(n + k)], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Error || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[1.084080291505059, -0.3914662527648858], NSum[Times[Power[k, -1], Power[Plus[1, k], -1], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]], Times[Complex[-0.8660254037844387, 0.49999999999999994], DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, 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[-1, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[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], BesselI[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Plus[Times[Power[1, -1], BesselI[0, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Times[Rational[-1, 2], Power[Plus[-1, 1], -1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], BesselI[1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][1.0]]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.001928095904955185, 0.0030033056761246957], Times[-1.0, NSum[Times[Power[k, -1], Power[Plus[2, k], -1], Plus[2, Times[2, k]], BesselI[Plus[2, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.44.E6 10.44.E6] || [[Item:Q3654|<math>\modBesselK{n}@{z} = \frac{n!(\tfrac{1}{2}z)^{-n}}{2}\sum_{k=0}^{n-1}(-1)^{k}\frac{(\tfrac{1}{2}z)^{k}\modBesselI{k}@{z}}{k!(n-k)}+(-1)^{n-1}\left(\ln@{\tfrac{1}{2}z}-\digamma@{n+1}\right)\modBesselI{n}@{z}+(-1)^{n}\sum_{k=1}^{\infty}\frac{(n+2k)\modBesselI{n+2k}@{z}}{k(n+k)}</math>]] || <code>BesselK(n, z) = (factorial(n)*((1)/(2)*z)^(- n))/(2)*sum((- 1)^(k)*(((1)/(2)*z)^(k)* BesselI(k, z))/(factorial(k)*(n - k)), k = 0..n - 1)+(- 1)^(n - 1)*(ln((1)/(2)*z)- Psi(n + 1))* BesselI(n, z)+(- 1)^(n)* sum(((n + 2*k)* BesselI(n + 2*k, z))/(k*(n + k)), k = 1..infinity)</code> || <code>BesselK[n, z] == Divide[(n)!*(Divide[1,2]*z)^(- n),2]*Sum[(- 1)^(k)*Divide[(Divide[1,2]*z)^(k)* BesselI[k, z],(k)!*(n - k)], {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n - 1)*(Log[Divide[1,2]*z]- PolyGamma[n + 1])* BesselI[n, z]+(- 1)^(n)* Sum[Divide[(n + 2*k)* BesselI[n + 2*k, z],k*(n + k)], {k, 1, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[1.084080291505059, -0.3914662527648858], NSum[Times[Power[k, -1], Power[Plus[1, k], -1], Plus[1, Times[2, k]], BesselI[Plus[1, Times[2, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {k, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]], Times[Complex[-0.8660254037844387, 0.49999999999999994], DifferenceRoot[Function[{, }, {Equal[Plus[Times[-1, 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[-1, , Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], 2]], Times[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[Po</div></div>
 |-
 | [https://dlmf.nist.gov/10.45.E1 10.45.E1] || [[Item:Q3655|<math>x^{2}\deriv[2]{w}{x}+x\deriv{w}{x}+(\nu^{2}-x^{2})w = 0</math>]] || <code>(x)^(2)* diff(w, [x$(2)])+ x*diff(w, x)+((nu)^(2)- (x)^(2))* w = 0</code> || <code>(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+(\[Nu]^(2)- (x)^(2))* w == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>240/300]: [[-1.948557159-.1249999996*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>-.2165063507+.8750000006*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.948557158514987, -0.12499999999999989] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.9485571585149875, -2.125] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 151: / Line 161: @@
 | [https://dlmf.nist.gov/10.47.E2 10.47.E2] || [[Item:Q3670|<math>z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}-\left(z^{2}+n(n+1)\right)w = 0</math>]] || <code>(z)^(2)* diff(w, [z$(2)])+ 2*z*diff(w, z)-((z)^(2)+ n*(n + 1))* w = 0</code> || <code>(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]-((z)^(2)+ n*(n + 1))* w == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>210/210]: [[-1.732050808-2.000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>-5.196152424-4.000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.7320508075688776, -1.9999999999999998] <- {Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-5.196152422706632, -3.9999999999999996] <- {Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.47.E3 10.47.E3] || [[Item:Q3671|<math>\sphBesselJ{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z]</code> || Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E3 10.47.E3] || [[Item:Q3671|<math>\sphBesselJ{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z]</code> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 21]
 |-
 | [https://dlmf.nist.gov/10.47.E3 10.47.E3] || [[Item:Q3671|<math>\sqrt{\tfrac{1}{2}\pi/z}\BesselJ{n+\frac{1}{2}}@{z} = (-1)^{n}\sqrt{\tfrac{1}{2}\pi/z}\BesselY{-n-\frac{1}{2}}@{z}</math>]] || <code>sqrt((1)/(2)*Pi/ z)*BesselJ(n +(1)/(2), z) = (- 1)^(n)*sqrt((1)/(2)*Pi/ z)*BesselY(- n -(1)/(2), z)</code> || <code>Sqrt[Divide[1,2]*Pi/ z]*BesselJ[n +Divide[1,2], z] == (- 1)^(n)*Sqrt[Divide[1,2]*Pi/ z]*BesselY[- n -Divide[1,2], z]</code> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47.E4 10.47.E4] || [[Item:Q3672|<math>\sphBesselY{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z]</code> || Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E4 10.47.E4] || [[Item:Q3672|<math>\sphBesselY{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z]</code> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 21]
 |-
 | [https://dlmf.nist.gov/10.47.E4 10.47.E4] || [[Item:Q3672|<math>\sqrt{\tfrac{1}{2}\pi/z}\BesselY{n+\frac{1}{2}}@{z} = (-1)^{n+1}\sqrt{\tfrac{1}{2}\pi/z}\BesselJ{-n-\frac{1}{2}}@{z}</math>]] || <code>sqrt((1)/(2)*Pi/ z)*BesselY(n +(1)/(2), z) = (- 1)^(n + 1)*sqrt((1)/(2)*Pi/ z)*BesselJ(- n -(1)/(2), z)</code> || <code>Sqrt[Divide[1,2]*Pi/ z]*BesselY[n +Divide[1,2], z] == (- 1)^(n + 1)*Sqrt[Divide[1,2]*Pi/ z]*BesselJ[- n -Divide[1,2], z]</code> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47.E5 10.47.E5] || [[Item:Q3673|<math>\sphHankelh{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z]</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E5 10.47.E5] || [[Item:Q3673|<math>\sphHankelh{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z]</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
 |-
 | [https://dlmf.nist.gov/10.47.E5 10.47.E5] || [[Item:Q3673|<math>\sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{n+\frac{1}{2}}@{z} = (-1)^{n+1}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{1}{-n-\frac{1}{2}}@{z}</math>]] || <code>sqrt((1)/(2)*Pi/ z)*HankelH1(n +(1)/(2), z) = (- 1)^(n + 1)* I*sqrt((1)/(2)*Pi/ z)*HankelH1(- n -(1)/(2), z)</code> || <code>Sqrt[Divide[1,2]*Pi/ z]*HankelH1[n +Divide[1,2], z] == (- 1)^(n + 1)* I*Sqrt[Divide[1,2]*Pi/ z]*HankelH1[- n -Divide[1,2], z]</code> || Successful || Failure || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47.E6 10.47.E6] || [[Item:Q3674|<math>\sphHankelh{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z]</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E6 10.47.E6] || [[Item:Q3674|<math>\sphHankelh{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z]</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
 |-
 | [https://dlmf.nist.gov/10.47.E6 10.47.E6] || [[Item:Q3674|<math>\sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{n+\frac{1}{2}}@{z} = (-1)^{n}\iunit\sqrt{\tfrac{1}{2}\pi/z}\HankelH{2}{-n-\frac{1}{2}}@{z}</math>]] || <code>sqrt((1)/(2)*Pi/ z)*HankelH2(n +(1)/(2), z) = (- 1)^(n)* I*sqrt((1)/(2)*Pi/ z)*HankelH2(- n -(1)/(2), z)</code> || <code>Sqrt[Divide[1,2]*Pi/ z]*HankelH2[n +Divide[1,2], z] == (- 1)^(n)* I*Sqrt[Divide[1,2]*Pi/ z]*HankelH2[- n -Divide[1,2], z]</code> || Successful || Failure || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47.E7 10.47.E7] || [[Item:Q3675|<math>\modsphBesseli{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == Sqrt[Divide[1,2]*Pi/ z]*BesselI[n +Divide[1,2], z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.47.E7 10.47.E7] || [[Item:Q3675|<math>\modsphBesseli{1}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == Sqrt[Divide[1,2]*Pi/ z]*BesselI[n +Divide[1,2], z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.47.E8 10.47.E8] || [[Item:Q3676|<math>\modsphBesseli{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{-n-\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Sqrt[Divide[1,2]*Pi/ z]*BesselI[- n -Divide[1,2], z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.41419719140728084, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1065867555175597, 2.4569570135519543] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.47.E8 10.47.E8] || [[Item:Q3676|<math>\modsphBesseli{2}{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselI{-n-\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Sqrt[Divide[1,2]*Pi/ z]*BesselI[- n -Divide[1,2], z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.41419719140728084, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1065867555175597, 2.4569570135519543] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.47.E9 10.47.E9] || [[Item:Q3677|<math>\modsphBesselK{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z]</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E9 10.47.E9] || [[Item:Q3677|<math>\modsphBesselK{n}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
 |-
 | [https://dlmf.nist.gov/10.47.E9 10.47.E9] || [[Item:Q3677|<math>\sqrt{\tfrac{1}{2}\pi/z}\modBesselK{n+\frac{1}{2}}@{z} = \sqrt{\tfrac{1}{2}\pi/z}\modBesselK{-n-\frac{1}{2}}@{z}</math>]] || <code>sqrt((1)/(2)*Pi/ z)*BesselK(n +(1)/(2), z) = sqrt((1)/(2)*Pi/ z)*BesselK(- n -(1)/(2), z)</code> || <code>Sqrt[Divide[1,2]*Pi/ z]*BesselK[n +Divide[1,2], z] == Sqrt[Divide[1,2]*Pi/ z]*BesselK[- n -Divide[1,2], z]</code> || Successful || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47#Ex1 10.47#Ex1] || [[Item:Q3678|<math>\sphHankelh{1}{n}@{z} = \sphBesselJ{n}@{z}+i\sphBesselY{n}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == SphericalBesselJ[n, z]+ I*SphericalBesselY[n, z]</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47#Ex1 10.47#Ex1] || [[Item:Q3678|<math>\sphHankelh{1}{n}@{z} = \sphBesselJ{n}@{z}+i\sphBesselY{n}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == SphericalBesselJ[n, z]+ I*SphericalBesselY[n, z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47#Ex2 10.47#Ex2] || [[Item:Q3679|<math>\sphHankelh{2}{n}@{z} = \sphBesselJ{n}@{z}-i\sphBesselY{n}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == SphericalBesselJ[n, z]- I*SphericalBesselY[n, z]</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47#Ex2 10.47#Ex2] || [[Item:Q3679|<math>\sphHankelh{2}{n}@{z} = \sphBesselJ{n}@{z}-i\sphBesselY{n}@{z}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == SphericalBesselJ[n, z]- I*SphericalBesselY[n, z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47.E11 10.47.E11] || [[Item:Q3680|<math>\modsphBesselK{n}@{z} = (-1)^{n+1}\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}-\modsphBesseli{2}{n}@{z}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n + 1)*Divide[1,2]*Pi*(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]- Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.7569924845794465, -0.925635877692591] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.0316385731075524, -4.1588442590402455] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.47.E11 10.47.E11] || [[Item:Q3680|<math>\modsphBesselK{n}@{z} = (-1)^{n+1}\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}-\modsphBesseli{2}{n}@{z}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n + 1)*Divide[1,2]*Pi*(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]- Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.7569924845794465, -0.925635877692591] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.0316385731075524, -4.1588442590402455] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.47#Ex3 10.47#Ex3] || [[Item:Q3681|<math>\modsphBesseli{1}{n}@{z} = i^{-n}\sphBesselJ{n}@{iz}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (I)^(- n)* SphericalBesselJ[n, I*z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965624, -0.2957981693651618] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.44982524194021284, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.47#Ex3 10.47#Ex3] || [[Item:Q3681|<math>\modsphBesseli{1}{n}@{z} = i^{-n}\sphBesselJ{n}@{iz}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (I)^(- n)* SphericalBesselJ[n, I*z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965624, -0.2957981693651618] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.44982524194021284, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.47#Ex4 10.47#Ex4] || [[Item:Q3682|<math>\modsphBesseli{2}{n}@{z} = i^{-n-1}\sphBesselY{n}@{iz}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == (I)^(- n - 1)* SphericalBesselY[n, I*z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.41419719140728045, -0.8850762711170859] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1065867555175588, 2.456957013551956] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.47#Ex4 10.47#Ex4] || [[Item:Q3682|<math>\modsphBesseli{2}{n}@{z} = i^{-n-1}\sphBesselY{n}@{iz}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == (I)^(- n - 1)* SphericalBesselY[n, I*z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.41419719140728045, -0.8850762711170859] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1065867555175588, 2.456957013551956] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.47.E13 10.47.E13] || [[Item:Q3683|<math>\modsphBesselK{n}@{z} = -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == -Divide[1,2]*Pi*(I)^(n)* SphericalHankelH1[n, I*z]</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E13 10.47.E13] || [[Item:Q3683|<math>\modsphBesselK{n}@{z} = -\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == -Divide[1,2]*Pi*(I)^(n)* SphericalHankelH1[n, I*z]</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.47.E13 10.47.E13] || [[Item:Q3683|<math>-\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz} = -\tfrac{1}{2}\pi i^{-n}\sphHankelh{2}{n}@{-iz}</math>]] || <code>Error</code> || <code>-Divide[1,2]*Pi*(I)^(n)* SphericalHankelH1[n, I*z] == -Divide[1,2]*Pi*(I)^(- n)* SphericalHankelH2[n, - I*z]</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.47.E13 10.47.E13] || [[Item:Q3683|<math>-\tfrac{1}{2}\pi i^{n}\sphHankelh{1}{n}@{iz} = -\tfrac{1}{2}\pi i^{-n}\sphHankelh{2}{n}@{-iz}</math>]] || <code>Error</code> || <code>-Divide[1,2]*Pi*(I)^(n)* SphericalHankelH1[n, I*z] == -Divide[1,2]*Pi*(I)^(- n)* SphericalHankelH2[n, - I*z]</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
 |-
 | [https://dlmf.nist.gov/10.47.E14 10.47.E14] || [[Item:Q3685|<math>\displaystyle\sphBesselJ{n}@{-z} = (-1)^{n}\sphBesselJ{n}@{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, - z] == (- 1)^(n)* SphericalBesselJ[n, z]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
@@ Line 201: / Line 211: @@
 | [https://dlmf.nist.gov/10.47.E16 10.47.E16] || [[Item:Q3689|<math>\displaystyle\modsphBesseli{2}{n}@{-z} = (-1)^{n+1}\modsphBesseli{2}{n}@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, - z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == (- 1)^(n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/10.47.E17 10.47.E17] || [[Item:Q3690|<math>\modsphBesselK{n}@{-z} = -\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}+\modsphBesseli{2}{n}@{z}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /- z] BesselK[n + 1/2, - z] == -Divide[1,2]*Pi*(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]+ Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.5442463690831921, -1.8549132335154932] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[2.444806248586177, 3.5599138449204935] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.47.E17 10.47.E17] || [[Item:Q3690|<math>\modsphBesselK{n}@{-z} = -\tfrac{1}{2}\pi\left(\modsphBesseli{1}{n}@{z}+\modsphBesseli{2}{n}@{z}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /- z] BesselK[n + 1/2, - z] == -Divide[1,2]*Pi*(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]+ Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.5442463690831921, -1.8549132335154932] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[2.444806248586177, 3.5599138449204935] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49.E2 10.49.E2] || [[Item:Q3692|<math>\sphBesselJ{n}@{z} = \sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.49.E2 10.49.E2] || [[Item:Q3692|<math>\sphBesselJ{n}@{z} = \sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.49#Ex1 10.49#Ex1] || [[Item:Q3693|<math>\sphBesselJ{0}@{z} = \frac{\sin@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[0, z] == Divide[Sin[z],z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex1 10.49#Ex1] || [[Item:Q3693|<math>\sphBesselJ{0}@{z} = \frac{\sin@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[0, z] == Divide[Sin[z],z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex2 10.49#Ex2] || [[Item:Q3694|<math>\sphBesselJ{1}@{z} = \frac{\sin@@{z}}{z^{2}}-\frac{\cos@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[1, z] == Divide[Sin[z],(z)^(2)]-Divide[Cos[z],z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex2 10.49#Ex2] || [[Item:Q3694|<math>\sphBesselJ{1}@{z} = \frac{\sin@@{z}}{z^{2}}-\frac{\cos@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[1, z] == Divide[Sin[z],(z)^(2)]-Divide[Cos[z],z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex3 10.49#Ex3] || [[Item:Q3695|<math>\sphBesselJ{2}@{z} = \left(-\frac{1}{z}+\frac{3}{z^{3}}\right)\sin@@{z}-\frac{3}{z^{2}}\cos@@{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[2, z] == (-Divide[1,z]+Divide[3,(z)^(3)])* Sin[z]-Divide[3,(z)^(2)]*Cos[z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex3 10.49#Ex3] || [[Item:Q3695|<math>\sphBesselJ{2}@{z} = \left(-\frac{1}{z}+\frac{3}{z^{3}}\right)\sin@@{z}-\frac{3}{z^{2}}\cos@@{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[2, z] == (-Divide[1,z]+Divide[3,(z)^(3)])* Sin[z]-Divide[3,(z)^(2)]*Cos[z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49.E4 10.49.E4] || [[Item:Q3696|<math>\sphBesselY{n}@{z} = -\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] == - Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.49.E4 10.49.E4] || [[Item:Q3696|<math>\sphBesselY{n}@{z} = -\cos@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+1}}+\sin@{z-\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] == - Cos[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 1)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[z -Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.49#Ex4 10.49#Ex4] || [[Item:Q3697|<math>\sphBesselY{0}@{z} = -\frac{\cos@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[0, z] == -Divide[Cos[z],z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex4 10.49#Ex4] || [[Item:Q3697|<math>\sphBesselY{0}@{z} = -\frac{\cos@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[0, z] == -Divide[Cos[z],z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex5 10.49#Ex5] || [[Item:Q3698|<math>\sphBesselY{1}@{z} = -\frac{\cos@@{z}}{z^{2}}-\frac{\sin@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[1, z] == -Divide[Cos[z],(z)^(2)]-Divide[Sin[z],z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex5 10.49#Ex5] || [[Item:Q3698|<math>\sphBesselY{1}@{z} = -\frac{\cos@@{z}}{z^{2}}-\frac{\sin@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[1, z] == -Divide[Cos[z],(z)^(2)]-Divide[Sin[z],z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex6 10.49#Ex6] || [[Item:Q3699|<math>\sphBesselY{2}@{z} = \left(\frac{1}{z}-\frac{3}{z^{3}}\right)\cos@@{z}-\frac{3}{z^{2}}\sin@@{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[2, z] == (Divide[1,z]-Divide[3,(z)^(3)])* Cos[z]-Divide[3,(z)^(2)]*Sin[z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex6 10.49#Ex6] || [[Item:Q3699|<math>\sphBesselY{2}@{z} = \left(\frac{1}{z}-\frac{3}{z^{3}}\right)\cos@@{z}-\frac{3}{z^{2}}\sin@@{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[2, z] == (Divide[1,z]-Divide[3,(z)^(3)])* Cos[z]-Divide[3,(z)^(2)]*Sin[z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49.E6 10.49.E6] || [[Item:Q3700|<math>\sphHankelh{1}{n}@{z} = e^{iz}\sum_{k=0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == Exp[I*z]*Sum[(I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-0.3966692432410339, 0.7497610210111748] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.3157223500929769, 0.5313692545383957] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49.E6 10.49.E6] || [[Item:Q3700|<math>\sphHankelh{1}{n}@{z} = e^{iz}\sum_{k=0}^{n}i^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == Exp[I*z]*Sum[(I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-0.3966692432410339, 0.7497610210111748] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.3157223500929769, 0.5313692545383957] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49.E7 10.49.E7] || [[Item:Q3701|<math>\sphHankelh{2}{n}@{z} = e^{-iz}\sum_{k=0}^{n}(-i)^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == Exp[- I*z]*Sum[(- I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.49.E7 10.49.E7] || [[Item:Q3701|<math>\sphHankelh{2}{n}@{z} = e^{-iz}\sum_{k=0}^{n}(-i)^{k-n-1}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == Exp[- I*z]*Sum[(- I)^(k - n - 1)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.49.E8 10.49.E8] || [[Item:Q3702|<math>\modsphBesseli{1}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n+1}\*\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n + 1)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.49.E8 10.49.E8] || [[Item:Q3702|<math>\modsphBesseli{1}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n+1}\*\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n + 1)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.49#Ex7 10.49#Ex7] || [[Item:Q3703|<math>\modsphBesseli{1}{0}@{z} = \frac{\sinh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(0 + 1/2), 0] == Divide[Sinh[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[-1.0789668887893185, -0.15155203743332835] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.9126970224666039, 0.13712305377128448] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex7 10.49#Ex7] || [[Item:Q3703|<math>\modsphBesseli{1}{0}@{z} = \frac{\sinh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(0 + 1/2), 0] == Divide[Sinh[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[-1.0789668887893185, -0.15155203743332835] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.9126970224666039, 0.13712305377128448] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex8 10.49#Ex8] || [[Item:Q3704|<math>\modsphBesseli{1}{1}@{z} = -\frac{\sinh@@{z}}{z^{2}}+\frac{\cosh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(1 + 1/2), 1] == -Divide[Sinh[z],(z)^(2)]+Divide[Cosh[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965646, -0.2957981693651617] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.3178790653897484, -0.6062561841669247] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex8 10.49#Ex8] || [[Item:Q3704|<math>\modsphBesseli{1}{1}@{z} = -\frac{\sinh@@{z}}{z^{2}}+\frac{\cosh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(1 + 1/2), 1] == -Divide[Sinh[z],(z)^(2)]+Divide[Cosh[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965646, -0.2957981693651617] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.3178790653897484, -0.6062561841669247] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex9 10.49#Ex9] || [[Item:Q3705|<math>\modsphBesseli{1}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\sinh@@{z}-\frac{3}{z^{2}}\cosh@@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)])* Sinh[z]-Divide[3,(z)^(2)]*Cosh[z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 7]<div class="mw-collapsible-content"><code>{Complex[0.44982524194021334, -0.19064547195046933] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.2843828483915114, -0.37732112452647515] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex9 10.49#Ex9] || [[Item:Q3705|<math>\modsphBesseli{1}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\sinh@@{z}-\frac{3}{z^{2}}\cosh@@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)])* Sinh[z]-Divide[3,(z)^(2)]*Cosh[z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 7]<div class="mw-collapsible-content"><code>{Complex[0.44982524194021334, -0.19064547195046933] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.2843828483915114, -0.37732112452647515] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49.E10 10.49.E10] || [[Item:Q3706|<math>\modsphBesseli{2}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n}\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.49.E10 10.49.E10] || [[Item:Q3706|<math>\modsphBesseli{2}{n}@{z} = \tfrac{1}{2}e^{z}\sum_{k=0}^{n}(-1)^{k}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}+(-1)^{n}\tfrac{1}{2}e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Divide[1,2]*Exp[z]*Sum[(- 1)^(k)*Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]+(- 1)^(n)*Divide[1,2]*(E)^(- z)* Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.49#Ex10 10.49#Ex10] || [[Item:Q3707|<math>\modsphBesseli{2}{0}@{z} = \frac{\cosh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(0 + 1/2), 0] == Divide[Cosh[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex10 10.49#Ex10] || [[Item:Q3707|<math>\modsphBesseli{2}{0}@{z} = \frac{\cosh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(0 + 1/2), 0] == Divide[Cosh[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>DirectedInfinity[] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex11 10.49#Ex11] || [[Item:Q3708|<math>\modsphBesseli{2}{1}@{z} = -\frac{\cosh@@{z}}{z^{2}}+\frac{\sinh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(1 + 1/2), 1] == -Divide[Cosh[z],(z)^(2)]+Divide[Sinh[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[-0.41419719140728073, -0.8850762711170859] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.1181398580617885, 1.2868595835312289] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex11 10.49#Ex11] || [[Item:Q3708|<math>\modsphBesseli{2}{1}@{z} = -\frac{\cosh@@{z}}{z^{2}}+\frac{\sinh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(1 + 1/2), 1] == -Divide[Cosh[z],(z)^(2)]+Divide[Sinh[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[-0.41419719140728073, -0.8850762711170859] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.1181398580617885, 1.2868595835312289] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex12 10.49#Ex12] || [[Item:Q3709|<math>\modsphBesseli{2}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\cosh@@{z}-\frac{3}{z^{2}}\sinh@@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)])* Cosh[z]-Divide[3,(z)^(2)]*Sinh[z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 7]<div class="mw-collapsible-content"><code>{Complex[1.106586755517561, 2.456957013551956] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.803584197807803, -1.2408087832280956] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex12 10.49#Ex12] || [[Item:Q3709|<math>\modsphBesseli{2}{2}@{z} = \left(\frac{1}{z}+\frac{3}{z^{3}}\right)\cosh@@{z}-\frac{3}{z^{2}}\sinh@@{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(2 + 1/2), 2] == (Divide[1,z]+Divide[3,(z)^(3)])* Cosh[z]-Divide[3,(z)^(2)]*Sinh[z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 7]<div class="mw-collapsible-content"><code>{Complex[1.106586755517561, 2.456957013551956] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.803584197807803, -1.2408087832280956] <- {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49.E12 10.49.E12] || [[Item:Q3710|<math>\modsphBesselK{n}@{z} = \tfrac{1}{2}\pi e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.0260307573251746, 0.0967341401667452] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.907697530268464, -0.43148595883398677] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49.E12 10.49.E12] || [[Item:Q3710|<math>\modsphBesselK{n}@{z} = \tfrac{1}{2}\pi e^{-z}\sum_{k=0}^{n}\frac{a_{k}(n+\frac{1}{2})}{z^{k+1}}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*Sum[Divide[Subscript[a, k]*(n +Divide[1,2]),(z)^(k + 1)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.0260307573251746, 0.0967341401667452] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.907697530268464, -0.43148595883398677] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex13 10.49#Ex13] || [[Item:Q3711|<math>\modsphBesselK{0}@{z} = \tfrac{1}{2}\pi\frac{e^{-z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[0 + 1/2, z] == Divide[1,2]*Pi*Divide[Exp[- z],z]</code> || Error || Failure || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex13 10.49#Ex13] || [[Item:Q3711|<math>\modsphBesselK{0}@{z} = \tfrac{1}{2}\pi\frac{e^{-z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[0 + 1/2, z] == Divide[1,2]*Pi*Divide[Exp[- z],z]</code> || Missing Macro Error || Failure || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex14 10.49#Ex14] || [[Item:Q3712|<math>\modsphBesselK{1}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{1}{z^{2}}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[1 + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[1,(z)^(2)])</code> || Error || Failure || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex14 10.49#Ex14] || [[Item:Q3712|<math>\modsphBesselK{1}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{1}{z^{2}}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[1 + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[1,(z)^(2)])</code> || Missing Macro Error || Failure || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex15 10.49#Ex15] || [[Item:Q3713|<math>\modsphBesselK{2}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{3}{z^{2}}+\frac{3}{z^{3}}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[2 + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[3,(z)^(2)]+Divide[3,(z)^(3)])</code> || Error || Failure || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex15 10.49#Ex15] || [[Item:Q3713|<math>\modsphBesselK{2}@{z} = \tfrac{1}{2}\pi e^{-z}\left(\frac{1}{z}+\frac{3}{z^{2}}+\frac{3}{z^{3}}\right)</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[2 + 1/2, z] == Divide[1,2]*Pi*Exp[- z]*(Divide[1,z]+Divide[3,(z)^(2)]+Divide[3,(z)^(3)])</code> || Missing Macro Error || Failure || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex16 10.49#Ex16] || [[Item:Q3714|<math>\sphBesselJ{n}@{z} = z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sin@@{z}}{z}</math>]] || <code>Error</code> || <code>(-Divide[1,z]*D[(z)^(n)*-Divide[1,z], z])^(n)*Divide[Sin[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.28766324258243325, 0.13393934480402792] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.302013441049254, 0.9125931496973667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex16 10.49#Ex16] || [[Item:Q3714|<math>\sphBesselJ{n}@{z} = z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sin@@{z}}{z}</math>]] || <code>Error</code> || <code>(-Divide[1,z]*D[(z)^(n)*-Divide[1,z], z])^(n)*Divide[Sin[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.28766324258243325, 0.13393934480402792] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.302013441049254, 0.9125931496973667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex17 10.49#Ex17] || [[Item:Q3715|<math>\sphBesselY{n}@{z} = -z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cos@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] (-Divide[1,z]*D[(z)^(n)*-Divide[1,z], z])^(n)*Divide[Cos[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.9342001374760677, 0.968266641946737] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.14357960272401077, 3.9384338499123404] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex17 10.49#Ex17] || [[Item:Q3715|<math>\sphBesselY{n}@{z} = -z^{n}\left(-\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cos@@{z}}{z}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] (-Divide[1,z]*D[(z)^(n)*-Divide[1,z], z])^(n)*Divide[Cos[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.9342001374760677, 0.968266641946737] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.14357960272401077, 3.9384338499123404] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex18 10.49#Ex18] || [[Item:Q3716|<math>\modsphBesseli{1}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sinh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] (Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Sinh[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.35534425318828616, -0.09521420567684166] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.19008700336701606, 0.7298484499303669] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex18 10.49#Ex18] || [[Item:Q3716|<math>\modsphBesseli{1}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\sinh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] (Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Sinh[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.35534425318828616, -0.09521420567684166] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.19008700336701606, 0.7298484499303669] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex19 10.49#Ex19] || [[Item:Q3717|<math>\modsphBesseli{2}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cosh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] (Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Cosh[z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.3553442531882861, 0.09521420567684165] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.31198506093225176, 1.0184810034762684] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49#Ex19 10.49#Ex19] || [[Item:Q3717|<math>\modsphBesseli{2}{n}@{z} = z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{\cosh@@{z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] (Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Cosh[z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.3553442531882861, 0.09521420567684165] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.31198506093225176, 1.0184810034762684] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49.E16 10.49.E16] || [[Item:Q3718|<math>\modsphBesselK{n}@{z} = (-1)^{n}\tfrac{1}{2}\pi z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{e^{-z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n)*Divide[1,2]*(Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Exp[- z],z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.3593544107322247, -1.2247601267643444] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.45891810409859557, -4.100723067341411] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49.E16 10.49.E16] || [[Item:Q3718|<math>\modsphBesselK{n}@{z} = (-1)^{n}\tfrac{1}{2}\pi z^{n}\left(\frac{1}{z}\deriv{}{z}\right)^{n}\frac{e^{-z}}{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == (- 1)^(n)*Divide[1,2]*(Divide[1,z]*D[(z)^(n)*Divide[1,z], z])^(n)*Divide[Exp[- z],z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.3593544107322247, -1.2247601267643444] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.45891810409859557, -4.100723067341411] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49.E18 10.49.E18] || [[Item:Q3720|<math>\sphBesselJ{n}^{2}@{z}+\sphBesselY{n}^{2}@{z} = \sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[n, z])^(2)+ (SphericalBesselY[n, z])^(2) == Sum[Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.2990381056766571, 0.5179491924311224] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-9.999999999999996, 1.5358983848622398] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49.E18 10.49.E18] || [[Item:Q3720|<math>\sphBesselJ{n}^{2}@{z}+\sphBesselY{n}^{2}@{z} = \sum_{k=0}^{n}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[n, z])^(2)+ (SphericalBesselY[n, z])^(2) == Sum[Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.2990381056766571, 0.5179491924311224] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-9.999999999999996, 1.5358983848622398] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.49#Ex20 10.49#Ex20] || [[Item:Q3721|<math>\sphBesselJ{0}^{2}@{z}+\sphBesselY{0}^{2}@{z} = z^{-2}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[0, z])^(2)+ (SphericalBesselY[0, z])^(2) == (z)^(- 2)</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex20 10.49#Ex20] || [[Item:Q3721|<math>\sphBesselJ{0}^{2}@{z}+\sphBesselY{0}^{2}@{z} = z^{-2}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[0, z])^(2)+ (SphericalBesselY[0, z])^(2) == (z)^(- 2)</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex21 10.49#Ex21] || [[Item:Q3722|<math>\sphBesselJ{1}^{2}@{z}+\sphBesselY{1}^{2}@{z} = z^{-2}+z^{-4}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[1, z])^(2)+ (SphericalBesselY[1, z])^(2) == (z)^(- 2)+ (z)^(- 4)</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex21 10.49#Ex21] || [[Item:Q3722|<math>\sphBesselJ{1}^{2}@{z}+\sphBesselY{1}^{2}@{z} = z^{-2}+z^{-4}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[1, z])^(2)+ (SphericalBesselY[1, z])^(2) == (z)^(- 2)+ (z)^(- 4)</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49#Ex22 10.49#Ex22] || [[Item:Q3723|<math>\sphBesselJ{2}^{2}@{z}+\sphBesselY{2}^{2}@{z} = z^{-2}+3z^{-4}+9z^{-6}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[2, z])^(2)+ (SphericalBesselY[2, z])^(2) == (z)^(- 2)+ 3*(z)^(- 4)+ 9*(z)^(- 6)</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.49#Ex22 10.49#Ex22] || [[Item:Q3723|<math>\sphBesselJ{2}^{2}@{z}+\sphBesselY{2}^{2}@{z} = z^{-2}+3z^{-4}+9z^{-6}</math>]] || <code>Error</code> || <code>(SphericalBesselJ[2, z])^(2)+ (SphericalBesselY[2, z])^(2) == (z)^(- 2)+ 3*(z)^(- 4)+ 9*(z)^(- 6)</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.49.E20 10.49.E20] || [[Item:Q3724|<math>\left(\modsphBesseli{1}{n}@{z}\right)^{2}-\left(\modsphBesseli{2}{n}@{z}\right)^{2} = (-1)^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n])^(2)-(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])^(2) == (- 1)^(n + 1)* Sum[(- 1)^(k)*Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.299038105676658, -0.7500000000000001] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.35182282028742856, 0.20312500000000058] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.49.E20 10.49.E20] || [[Item:Q3724|<math>\left(\modsphBesseli{1}{n}@{z}\right)^{2}-\left(\modsphBesseli{2}{n}@{z}\right)^{2} = (-1)^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{s_{k}(n+\frac{1}{2})}{z^{2k+2}}</math>]] || <code>Error</code> || <code>(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n])^(2)-(Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n])^(2) == (- 1)^(n + 1)* Sum[(- 1)^(k)*Divide[Subscript[s, k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-1.299038105676658, -0.7500000000000001] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.35182282028742856, 0.20312500000000058] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.50#Ex1 10.50#Ex1] || [[Item:Q3728|<math>\Wronskian@{\sphBesselJ{n}@{z},\sphBesselY{n}@{z}} = z^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{SphericalBesselJ[n, z], SphericalBesselY[n, z]}, z] == (z)^(- 2)</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.50#Ex1 10.50#Ex1] || [[Item:Q3728|<math>\Wronskian@{\sphBesselJ{n}@{z},\sphBesselY{n}@{z}} = z^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{SphericalBesselJ[n, z], SphericalBesselY[n, z]}, z] == (z)^(- 2)</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.50#Ex2 10.50#Ex2] || [[Item:Q3729|<math>\Wronskian@{\sphHankelh{1}{n}@{z},\sphHankelh{2}{n}@{z}} = -2iz^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{SphericalHankelH1[n, z], SphericalHankelH2[n, z]}, z] == - 2*I*(z)^(- 2)</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.50#Ex2 10.50#Ex2] || [[Item:Q3729|<math>\Wronskian@{\sphHankelh{1}{n}@{z},\sphHankelh{2}{n}@{z}} = -2iz^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{SphericalHankelH1[n, z], SphericalHankelH2[n, z]}, z] == - 2*I*(z)^(- 2)</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.50#Ex3 10.50#Ex3] || [[Item:Q3730|<math>\Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesseli{2}{n}@{z}} = (-1)^{n+1}z^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]}, z] == (- 1)^(n + 1)* (z)^(- 2)</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.5000000000000001, 0.8660254037844386] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.5000000000000001, -0.8660254037844386] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.50#Ex3 10.50#Ex3] || [[Item:Q3730|<math>\Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesseli{2}{n}@{z}} = (-1)^{n+1}z^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n]}, z] == (- 1)^(n + 1)* (z)^(- 2)</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.5000000000000001, 0.8660254037844386] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.5000000000000001, -0.8660254037844386] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.50#Ex4 10.50#Ex4] || [[Item:Q3731|<math>\Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesselK{n}@{z}} = \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\</math>]] || <code>Error</code> || <code>Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.5384915109869794, 1.7026856201657974] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.6544302063904848, -2.4451654315616667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.50#Ex4 10.50#Ex4] || [[Item:Q3731|<math>\Wronskian@{\modsphBesseli{1}{n}@{z},\modsphBesselK{n}@{z}} = \Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\</math>]] || <code>Error</code> || <code>Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.5384915109869794, 1.7026856201657974] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.6544302063904848, -2.4451654315616667] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.50#Ex4 10.50#Ex4] || [[Item:Q3731|<math>\Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\ = -\tfrac{1}{2}\pi z^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == -Divide[1,2]*Pi*(z)^(- 2)</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.5161524079039588, -2.211692333258562] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[7.686727830477982, 4.996906619076774] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.50#Ex4 10.50#Ex4] || [[Item:Q3731|<math>\Wronskian@{\modsphBesseli{2}{n}@{z},\modsphBesselK{n}@{z}}\\ = -\tfrac{1}{2}\pi z^{-2}</math>]] || <code>Error</code> || <code>Wronskian[{Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n], Sqrt[1/2 Pi /z] BesselK[n + 1/2, z]}, z] == -Divide[1,2]*Pi*(z)^(- 2)</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.5161524079039588, -2.211692333258562] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[7.686727830477982, 4.996906619076774] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.50#Ex5 10.50#Ex5] || [[Item:Q3732|<math>\sphBesselJ{n+1}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+1}@{z} = z^{-2}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n + 1, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 1, z] == (z)^(- 2)</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.50#Ex5 10.50#Ex5] || [[Item:Q3732|<math>\sphBesselJ{n+1}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+1}@{z} = z^{-2}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n + 1, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 1, z] == (z)^(- 2)</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.50#Ex6 10.50#Ex6] || [[Item:Q3733|<math>\sphBesselJ{n+2}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+2}@{z} = (2n+3)z^{-3}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n + 2, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 2, z] == (2*n + 3)* (z)^(- 3)</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.50#Ex6 10.50#Ex6] || [[Item:Q3733|<math>\sphBesselJ{n+2}@{z}\sphBesselY{n}@{z}-\sphBesselJ{n}@{z}\sphBesselY{n+2}@{z} = (2n+3)z^{-3}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n + 2, z]*SphericalBesselY[n, z]- SphericalBesselJ[n, z]*SphericalBesselY[n + 2, z] == (2*n + 3)* (z)^(- 3)</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/10.50.E4 10.50.E4] || [[Item:Q3734|<math>\sphBesselJ{0}@{z}\sphBesselJ{n}@{z}+\sphBesselY{0}@{z}\sphBesselY{n}@{z} = \cos@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+2}}+\sin@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+3}}</math>]] || <code>Error</code> || <code>SphericalBesselJ[0, z]*SphericalBesselJ[n, z]+ SphericalBesselY[0, z]*SphericalBesselY[n, z] == Cos[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 3)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.50.E4 10.50.E4] || [[Item:Q3734|<math>\sphBesselJ{0}@{z}\sphBesselJ{n}@{z}+\sphBesselY{0}@{z}\sphBesselY{n}@{z} = \cos@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{n/2}}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+2}}+\sin@{\tfrac{1}{2}n\pi}\sum_{k=0}^{\floor{(n-1)/2}}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+3}}</math>]] || <code>Error</code> || <code>SphericalBesselJ[0, z]*SphericalBesselJ[n, z]+ SphericalBesselY[0, z]*SphericalBesselY[n, z] == Cos[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k]*(n +Divide[1,2]),(z)^(2*k + 2)], {k, 0, Floor[n/ 2]}, GenerateConditions->None]+ Sin[Divide[1,2]*n*Pi]*Sum[(- 1)^(k)*Divide[Subscript[a, 2*k + 1]*(n +Divide[1,2]),(z)^(2*k + 3)], {k, 0, Floor[(n - 1)/ 2]}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.51#Ex1 10.51#Ex1] || [[Item:Q3735|<math>f_{n-1}(z)+f_{n+1}(z) = ((2n+1)/z)f_{n}(z)</math>]] || <code>f[n - 1]*(z)+ f[n + 1]*(z) = ((2*n + 1)/ z)* f[n]*(z)</code> || <code>Subscript[f, n - 1]*(z)+ Subscript[f, n + 1]*(z) == ((2*n + 1)/ z)* Subscript[f, n]*(z)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
@@ Line 295: / Line 305: @@
 | [https://dlmf.nist.gov/10.51#Ex12 10.51#Ex12] || [[Item:Q3746|<math>\left(\frac{1}{z}\deriv{}{z}\right)^{m}(z^{-n}g_{n}(z)) = z^{-n-m}g_{n+m}(z)</math>]] || <code>(diff((1)/(z), z))^(m)*((z)^(- n)* g[n]*(z)) = (z)^(- n - m)* g[n + m]*(z)</code> || <code>(D[Divide[1,z], z])^(m)*((z)^(- n)* Subscript[g, n]*(z)) == (z)^(- n - m)* Subscript[g, n + m]*(z)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [288 / 300]<div class="mw-collapsible-content"><code>288/300]: [[.3660254028+1.366025403*I <- {z = 1/2*3^(1/2)+1/2*I, g[n] = 1/2*3^(1/2)+1/2*I, g[n+m] = 1/2*3^(1/2)+1/2*I, n = 1, m = 3}</code><br><code>.9999999987+.9999999996*I <- {z = 1/2*3^(1/2)+1/2*I, g[n] = 1/2*3^(1/2)+1/2*I, g[n+m] = 1/2*3^(1/2)+1/2*I, n = 2, m = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [288 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.8660254037844388, 0.49999999999999994] <- {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.3660254037844388, 1.3660254037844386] <- {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[m, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.53.E1 10.53.E1] || [[Item:Q3755|<math>\sphBesselJ{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == (z)^(n)* Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.53.E1 10.53.E1] || [[Item:Q3755|<math>\sphBesselJ{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == (z)^(n)* Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
+|-
+| [https://dlmf.nist.gov/10.53.E2 10.53.E2] || [[Item:Q3756|<math>\sphBesselY{n}@{z} = -\frac{1}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(\frac{1}{2}z^{2})^{k}}{k!}+\frac{(-1)^{n+1}}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] == -Divide[1,(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[(- 1)^(n + 1),(z)^(n + 1)]*Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Successful [Tested: 21]
+|-
+| [https://dlmf.nist.gov/10.53.E3 10.53.E3] || [[Item:Q3757|<math>\modsphBesseli{1}{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (z)^(n)* Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.53.E4 10.53.E4] || [[Item:Q3758|<math>\modsphBesseli{2}{n}@{z} = \frac{(-1)^{n}}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(-\frac{1}{2}z^{2})^{k}}{k!}+\frac{1}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Divide[(- 1)^(n),(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(-Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[1,(z)^(n + 1)]*Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.4141971914072808, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1065867555175597, 2.456957013551954] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.54.E1 10.54.E1] || [[Item:Q3759|<math>\sphBesselJ{n}@{z} = \frac{z^{n}}{2^{n+1}n!}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2n+1}\diff{\theta}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Divide[(z)^(n),(2)^(n + 1)* (n)!]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*n + 1), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Missing Macro Error || Successful || - || Successful [Tested: 21]
+|-
+| [https://dlmf.nist.gov/10.54.E2 10.54.E2] || [[Item:Q3760|<math>\sphBesselJ{n}@{z} = \frac{(-i)^{n}}{2}\int_{0}^{\pi}e^{iz\cos@@{\theta}}\assLegendreP[]{n}@{\cos@@{\theta}}\sin@@{\theta}\diff{\theta}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Divide[(- I)^(n),2]*Integrate[Exp[I*z*Cos[\[Theta]]]*LegendreP[n, 0, 3, Cos[\[Theta]]]*Sin[\[Theta]], {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || Successful [Tested: 21]
+|-
+| [https://dlmf.nist.gov/10.54.E3 10.54.E3] || [[Item:Q3761|<math>\modsphBesselK{n}@{z} = \frac{\pi}{2}\int_{1}^{\infty}e^{-zt}\assLegendreP[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /z] BesselK[n + 1/2, z] == Divide[Pi,2]*Integrate[Exp[- z*t]*LegendreP[n, 0, 3, t], {t, 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || Skipped - Because timed out
+|-
+| [https://dlmf.nist.gov/10.54.E4 10.54.E4] || [[Item:Q3762|<math>\sphBesselJ{n}@{z} = \frac{(-i)^{n+1}}{2\pi}\int_{i\infty}^{(-1+,1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Divide[(- I)^(n + 1),2*Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 + , 1 +)}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Error
+|-
+| [https://dlmf.nist.gov/10.54#Ex1 10.54#Ex1] || [[Item:Q3763|<math>\sphHankelh{1}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (1 +)}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/10.53.E2 10.53.E2] || [[Item:Q3756|<math>\sphBesselY{n}@{z} = -\frac{1}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(\frac{1}{2}z^{2})^{k}}{k!}+\frac{(-1)^{n+1}}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(-\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, z] == -Divide[1,(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[(- 1)^(n + 1),(z)^(n + 1)]*Sum[Divide[(-Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.54#Ex2 10.54#Ex2] || [[Item:Q3764|<math>\sphHankelh{2}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(-1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 +)}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Error
 |-
-| [https://dlmf.nist.gov/10.53.E3 10.53.E3] || [[Item:Q3757|<math>\modsphBesseli{1}{n}@{z} = z^{n}\sum_{k=0}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2n+2k+1)!!}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n] == (z)^(n)* Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*n + 2*k + 1)!!], {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[0.06771919180965624, -0.29579816936516184] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.4498252419402129, -0.19064547195046921] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.56.E1 10.56.E1] || [[Item:Q3765|<math>\frac{\cos@@{\sqrt{z^{2}-2zt}}}{z} = \frac{\cos@@{z}}{z}+\sum_{n=1}^{\infty}\frac{t^{n}}{n!}\sphBesselJ{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Cos[Sqrt[(z)^(2)- 2*z*t]],z] == Divide[Cos[z],z]+ Sum[Divide[(t)^(n),(n)!]*SphericalBesselJ[n - 1, z], {n, 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><code>{Plus[Complex[-1.0653161526495918, 0.32810386977400907], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-1.8246723112251149, 0.13108435615091096], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.53.E4 10.53.E4] || [[Item:Q3758|<math>\modsphBesseli{2}{n}@{z} = \frac{(-1)^{n}}{z^{n+1}}\sum_{k=0}^{n}\frac{(2n-2k-1)!!(-\frac{1}{2}z^{2})^{k}}{k!}+\frac{1}{z^{n+1}}\sum_{k=n+1}^{\infty}\frac{(\frac{1}{2}z^{2})^{k}}{k!(2k-2n-1)!!}</math>]] || <code>Error</code> || <code>Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n + 1/2), n] == Divide[(- 1)^(n),(z)^(n + 1)]*Sum[Divide[(2*n - 2*k - 1)!!*(-Divide[1,2]*(z)^(2))^(k),(k)!], {k, 0, n}, GenerateConditions->None]+Divide[1,(z)^(n + 1)]*Sum[Divide[(Divide[1,2]*(z)^(2))^(k),(k)!*(2*k - 2*n - 1)!!], {k, n + 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><code>{Complex[-0.4141971914072808, -0.8850762711170854] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1065867555175597, 2.456957013551954] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.56.E2 10.56.E2] || [[Item:Q3766|<math>\frac{\sin@@{\sqrt{z^{2}-2zt}}}{z} = \frac{\sin@@{z}}{z}+\sum_{n=1}^{\infty}\frac{t^{n}}{n!}\sphBesselY{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Sin[Sqrt[(z)^(2)- 2*z*t]],z] == Divide[Sin[z],z]+ Sum[Divide[(t)^(n),(n)!]*SphericalBesselY[n - 1, z], {n, 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.54.E1 10.54.E1] || [[Item:Q3759|<math>\sphBesselJ{n}@{z} = \frac{z^{n}}{2^{n+1}n!}\int_{0}^{\pi}\cos@{z\cos@@{\theta}}(\sin@@{\theta})^{2n+1}\diff{\theta}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Divide[(z)^(n),(2)^(n + 1)* (n)!]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*n + 1), {\[Theta], 0, Pi}, GenerateConditions->None]</code> || Error || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/10.56.E3 10.56.E3] || [[Item:Q3767|<math>\frac{\cosh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\cosh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{1}{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Cosh[Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Cosh[z],z]+ Sum[Divide[(I*t)^(n),(n)!]*Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.13108435615091052, -1.8246723112251153], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.022834987510423566, -1.7127448295681993], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.54.E4 10.54.E4] || [[Item:Q3762|<math>\sphBesselJ{n}@{z} = \frac{(-i)^{n+1}}{2\pi}\int_{i\infty}^{(-1+,1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, z] == Divide[(- I)^(n + 1),2*Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 + , 1 +)}, GenerateConditions->None]</code> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/10.56.E4 10.56.E4] || [[Item:Q3768|<math>\frac{\sinh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\sinh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{2}{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Sinh[Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Sinh[z],z]+ Sum[Divide[(I*t)^(n),(n)!]*Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.12983798012989667, -2.1935922908985273], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-1.4886830119296848, -1.839102010336905], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.54#Ex1 10.54#Ex1] || [[Item:Q3763|<math>\sphHankelh{1}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>SphericalHankelH1[n, z] == Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (1 +)}, GenerateConditions->None]</code> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/10.56.E5 10.56.E5] || [[Item:Q3769|<math>\frac{\exp@{-\sqrt{z^{2}+2izt}}}{z} = \frac{e^{-z}}{z}+\frac{2}{\pi}\sum_{n=1}^{\infty}\frac{(-it)^{n}}{n!}\modsphBesselK{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Exp[-Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Exp[- z],z]+Divide[2,Pi]*Sum[Divide[(- I*t)^(n),(n)!]*Sqrt[1/2 Pi /z] BesselK[n - 1 + 1/2, z], {n, 1, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.54#Ex2 10.54#Ex2] || [[Item:Q3764|<math>\sphHankelh{2}{n}@{z} = \frac{(-i)^{n+1}}{\pi}\int_{i\infty}^{(-1+)}e^{izt}\assLegendreQ[]{n}@{t}\diff{t}</math>]] || <code>Error</code> || <code>SphericalHankelH2[n, z] == Divide[(- I)^(n + 1),Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 1 +)}, GenerateConditions->None]</code> || Error || Failure || - || Error
+| [https://dlmf.nist.gov/10.57.E1 10.57.E1] || [[Item:Q3770|<math>\sphBesselJ{n}'@{(n+\tfrac{1}{2})z} = \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}\BesselJ{n+\frac{1}{2}}'@{(n+\tfrac{1}{2})z}-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}\BesselJ{n+\frac{1}{2}}@{(n+\tfrac{1}{2})z}</math>]] || <code>Error</code> || <code>D[SphericalBesselJ[n, (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}] == Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[1,2])]*D[BesselJ[n +Divide[1,2], (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}]-Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[3,2])]*BesselJ[n +Divide[1,2], (n +Divide[1,2])* z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.14653389603833195, -0.029869009956249915], Times[Complex[-0.988457695936884, 0.2648564413786163], D[Complex[0.36567703182522004, 0.24184221354059504] <- {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], D[Complex[0.425509744388485, 0.14219887983348967], {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.06710374092328811, 0.007963502819859997], Times[Complex[-0.7656560389588212, 0.20515691731902835], D[Complex[0.2637838125883578, 0.3348231997381719] <- {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], D[Complex[0.27065896459303473, 0.20224233103375913], {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.56.E1 10.56.E1] || [[Item:Q3765|<math>\frac{\cos@@{\sqrt{z^{2}-2zt}}}{z} = \frac{\cos@@{z}}{z}+\sum_{n=1}^{\infty}\frac{t^{n}}{n!}\sphBesselJ{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Cos[Sqrt[(z)^(2)- 2*z*t]],z] == Divide[Cos[z],z]+ Sum[Divide[(t)^(n),(n)!]*SphericalBesselJ[n - 1, z], {n, 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><code>{Plus[Complex[-1.0653161526495918, 0.32810386977400907], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-1.8246723112251149, 0.13108435615091096], Times[-1.0, NSum[Times[Power[-1.5, n], Power[Factorial[n], -1], SphericalBesselJ[Plus[-1, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E1 10.60.E1] || [[Item:Q3776|<math>\frac{\cos@@{w}}{w} = -\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselY{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Divide[Cos[w],w] == - Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselY[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.56.E3 10.56.E3] || [[Item:Q3767|<math>\frac{\cosh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\cosh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{1}{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Cosh[Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Cosh[z],z]+ Sum[Divide[(I*t)^(n),(n)!]*Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.13108435615091052, -1.8246723112251153], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.022834987510423566, -1.7127448295681993], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[-1, 2], n], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E2 10.60.E2] || [[Item:Q3777|<math>\frac{\sin@@{w}}{w} = \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselJ{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Divide[Sin[w],w] == Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselJ[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.56.E4 10.56.E4] || [[Item:Q3768|<math>\frac{\sinh@@{\sqrt{z^{2}+2izt}}}{z} = \frac{\sinh@@{z}}{z}+\sum_{n=1}^{\infty}\frac{(it)^{n}}{n!}\modsphBesseli{2}{n-1}@{z}</math>]] || <code>Error</code> || <code>Divide[Sinh[Sqrt[(z)^(2)+ 2*I*z*t]],z] == Divide[Sinh[z],z]+ Sum[Divide[(I*t)^(n),(n)!]*Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(2-1)*(n - 1 + 1/2), n - 1], {n, 1, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.12983798012989667, -2.1935922908985273], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-1.4886830119296848, -1.839102010336905], Times[-1.0, NSum[Times[Power[Complex[0.0, -1.5], n], Power[Power[E, Times[Complex[0, Rational[-2, 3]], Pi]], Rational[1, 2]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], Times[-1, n]], Plus[-1, n]], Power[Factorial[n], -1]] <- {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E3 10.60.E3] || [[Item:Q3778|<math>\frac{e^{-w}}{w} = \frac{2}{\pi}\sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{v}\modsphBesselK{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Divide[Exp[- w],w] == Divide[2,Pi]*Sum[(2*n + 1)* Sqrt[Divide[Pi, v]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*Sqrt[1/2 Pi /u] BesselK[n + 1/2, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.57.E1 10.57.E1] || [[Item:Q3770|<math>\sphBesselJ{n}'@{(n+\tfrac{1}{2})z} = \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}\BesselJ{n+\frac{1}{2}}'@{(n+\tfrac{1}{2})z}-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}\BesselJ{n+\frac{1}{2}}@{(n+\tfrac{1}{2})z}</math>]] || <code>Error</code> || <code>D[SphericalBesselJ[n, (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}] == Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[1,2])]*D[BesselJ[n +Divide[1,2], (n +Divide[1,2])* z], {(n +Divide[1,2])* z, 1}]-Divide[(Pi)^(Divide[1,2]),((2*n + 1)*z)^(Divide[3,2])]*BesselJ[n +Divide[1,2], (n +Divide[1,2])* z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.14653389603833195, -0.029869009956249915], Times[Complex[-0.988457695936884, 0.2648564413786163], D[Complex[0.36567703182522004, 0.24184221354059504] <- {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], D[Complex[0.425509744388485, 0.14219887983348967], {Complex[1.299038105676658, 0.7499999999999999], 1.0}]], {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.06710374092328811, 0.007963502819859997], Times[Complex[-0.7656560389588212, 0.20515691731902835], D[Complex[0.2637838125883578, 0.3348231997381719] <- {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], D[Complex[0.27065896459303473, 0.20224233103375913], {Complex[2.165063509461097, 1.2499999999999998], 1.0}]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E4 10.60.E4] || [[Item:Q3779|<math>\sphBesselJ{n}@{2z} = -n!z^{n+1}\sum_{k=0}^{n}\frac{2n-2k+1}{k!(2n-k+1)!}\sphBesselJ{n-k}@{z}\sphBesselY{n-k}@{z}</math>]] || <code>Error</code> || <code>SphericalBesselJ[n, 2*z] == - (n)!*(z)^(n + 1)* Sum[Divide[2*n - 2*k + 1,(k)!*(2*n - k + 1)!]*SphericalBesselJ[n - k, z]*SphericalBesselY[n - k, z], {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><code>{Plus[0.3456774997623559, Times[2.25, Plus[Times[-2.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[-3, Times[-2, ], Times[2, 1]], Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[1, Times[-1, ], Times[2, 1]], Power[1.5, 2], []], Times[-1, Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[Times[-3, ], Times[-14, Power[, 2]], Times[-20, Power[, 3]], Times[-8, Power[, 4]], Times[14, , 1], Times[40, Power[, 2], 1], Times[24, Power[, 3], 1], Times[-20, , Power[1, 2]], Times[-24, Power[, 2], Power[1, 2]], Times[8, , Power[1, 3]], Times[-3, Power[1.5, 2]], Times[2, , Power[1.5, 2]], Times[4, Power[, 2], Power[1.5, 2]], Times[-4, 1, Power[1.5, 2]], Times[-8, , 1, Power[1.5, 2]], Times[4, Power[1, 2], Power[1.5, 2]]], [Plus[1, ]]], Times[, Plus[1, , Times[-2, 1]], Plus[3, Times[4, ], Times[4, , 1], Times[-4, Power[1, 2]]], Plus[3, Times[8, ], Times[4, Power[, 2]], Times[-8, 1], Times[-8, , 1], Times[</div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E1 10.60.E1] || [[Item:Q3776|<math>\frac{\cos@@{w}}{w} = -\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselY{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Divide[Cos[w],w] == - Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselY[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.43419403794642014, -0.7090399040477617], NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, -0.5], SphericalBesselY[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, -0.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E5 10.60.E5] || [[Item:Q3780|<math>\sphBesselY{n}@{2z} = n!z^{n+1}\sum_{k=0}^{n}\frac{n-k+\frac{1}{2}}{k!(2n-k+1)!}{\left(\sphBesselJ{n-k}^{2}@{z}-\sphBesselY{n-k}^{2}@{z}\right)}</math>]] || <code>Error</code> || <code>SphericalBesselY[n, 2*z] == (n)!*(z)^(n + 1)* Sum[Divide[n - k +Divide[1,2],(k)!*(2*n - k + 1)!]*((SphericalBesselJ[n - k, z])^(2)- (SphericalBesselY[n - k, z])^(2)), {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><code>{Plus[0.06295916360231597, Times[-1.125, Plus[Times[-2.0, DifferenceRoot[Function[{, } <- {Equal[Plus[Times[Plus[-3, Times[-2, ], Times[2, 1]], Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[1, Times[-1, ], Times[2, 1]], Power[1.5, 2], []], Times[-1, Plus[-1, Times[-1, ], Times[2, 1]], Plus[Times[-1, ], Times[2, 1]], Plus[Times[-3, ], Times[-14, Power[, 2]], Times[-20, Power[, 3]], Times[-8, Power[, 4]], Times[14, , 1], Times[40, Power[, 2], 1], Times[24, Power[, 3], 1], Times[-20, , Power[1, 2]], Times[-24, Power[, 2], Power[1, 2]], Times[8, , Power[1, 3]], Times[-3, Power[1.5, 2]], Times[2, , Power[1.5, 2]], Times[4, Power[, 2], Power[1.5, 2]], Times[-4, 1, Power[1.5, 2]], Times[-8, , 1, Power[1.5, 2]], Times[4, Power[1, 2], Power[1.5, 2]]], [Plus[1, ]]], Times[, Plus[1, , Times[-2, 1]], Plus[3, Times[4, ], Times[4, , 1], Times[-4, Power[1, 2]]], Plus[3, Times[8, ], Times[4, Power[, 2]], Times[-8, 1], Times[-8, , 1], Tim</div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E2 10.60.E2] || [[Item:Q3777|<math>\frac{\sin@@{w}}{w} = \sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}@{v}\sphBesselJ{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Divide[Sin[w],w] == Sum[(2*n + 1)* SphericalBesselJ[n, v]*SphericalBesselJ[n, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.912697022466604, -0.13712305377128448], Times[-1.0, NSum[Times[Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E6 10.60.E6] || [[Item:Q3781|<math>\modsphBesselK{n}@{2z} = \frac{1}{\pi}n!z^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{2n-2k+1}{k!(2n-k+1)!}\modsphBesselK{n-k}^{2}@{z}</math>]] || <code>Error</code> || <code>Sqrt[1/2 Pi /2*z] BesselK[n + 1/2, 2*z] == Divide[1,Pi]*(n)!*(z)^(n + 1)* Sum[(- 1)^(k)*Divide[2*n - 2*k + 1,(k)!*(2*n - k + 1)!]*(Sqrt[1/2 Pi /z] BesselK[n - k + 1/2, z])^(2), {k, 0, n}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Complex[0.10365998143807895, 0.01421463603104145] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.21384035370849797, -0.0374061947505589] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E3 10.60.E3] || [[Item:Q3778|<math>\frac{e^{-w}}{w} = \frac{2}{\pi}\sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{v}\modsphBesselK{n}@{u}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Divide[Exp[- w],w] == Divide[2,Pi]*Sum[(2*n + 1)* Sqrt[Divide[Pi, v]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*Sqrt[1/2 Pi /u] BesselK[n + 1/2, u]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.60.E7 10.60.E7] || [[Item:Q3782|<math>e^{iz\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)i^{n}\sphBesselJ{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Exp[I*z*Cos[\[Alpha]]] == Sum[(2*n + 1)* (I)^(n)* SphericalBesselJ[n, z]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.9634389243184156, 0.05909441627762202], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.46738148067268087, 0.44423123280344756], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E7 10.60.E7] || [[Item:Q3782|<math>e^{iz\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)i^{n}\sphBesselJ{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Exp[I*z*Cos[\[Alpha]]] == Sum[(2*n + 1)* (I)^(n)* SphericalBesselJ[n, z]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.9634389243184156, 0.05909441627762202], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.0707372016677029], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.46738148067268087, 0.44423123280344756], Times[-1.0, NSum[Times[Power[Complex[0, 1], n], Plus[1, Times[2, n]], LegendreP[n, 0.8775825618903728], SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E8 10.60.E8] || [[Item:Q3783|<math>e^{z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Exp[z*Cos[\[Alpha]]] == Sum[(2*n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[1.0625106169893304, 0.037595191618525974], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[1.935725445820811, 0.9084451535292719], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E8 10.60.E8] || [[Item:Q3783|<math>e^{z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Exp[z*Cos[\[Alpha]]] == Sum[(2*n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[1.0625106169893304, 0.037595191618525974], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[1.935725445820811, 0.9084451535292719], Times[-1.0, NSum[Times[Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E9 10.60.E9] || [[Item:Q3784|<math>e^{-z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Exp[- z*Cos[\[Alpha]]] == Sum[(- 1)^(n)*(2*n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.939990215282077, -0.03326000860415312], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.4233587200353881, -0.19868425982147583], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E9 10.60.E9] || [[Item:Q3784|<math>e^{-z\cos@@{\alpha}} = \sum_{n=0}^{\infty}(-1)^{n}(2n+1)\modsphBesseli{1}{n}@{z}\assLegendreP[]{n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>Exp[- z*Cos[\[Alpha]]] == Sum[(- 1)^(n)*(2*n + 1)* Sqrt[Divide[Pi, z]/2] BesselI[(-1)^(1-1)*(n + 1/2), n]*LegendreP[n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.939990215282077, -0.03326000860415312], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.0707372016677029]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.4233587200353881, -0.19868425982147583], Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[-1, 6]], Pi]], Rational[1, 2]], Plus[1, Times[2, n]], Power[Times[Rational[1, 2], Pi], Rational[1, 2]], BesselI[Plus[Rational[1, 2], n], n], LegendreP[n, 0.8775825618903728]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E10 10.60.E10] || [[Item:Q3785|<math>\BesselJ{0}@{z\sin@@{\alpha}} = \sum_{n=0}^{\infty}(4n+1)\frac{(2n)!}{2^{2n}(n!)^{2}}\sphBesselJ{2n}@{z}\assLegendreP[]{2n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>BesselJ[0, z*Sin[\[Alpha]]] == Sum[(4*n + 1)*Divide[(2*n)!,(2)^(2*n)*((n)!)^(2)]*SphericalBesselJ[2*n, z]*LegendreP[2*n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.8683151459050518, -0.20203213835937428], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.0707372016677029], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.9708614168197589, -0.04904886793011446], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.8775825618903728], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E10 10.60.E10] || [[Item:Q3785|<math>\BesselJ{0}@{z\sin@@{\alpha}} = \sum_{n=0}^{\infty}(4n+1)\frac{(2n)!}{2^{2n}(n!)^{2}}\sphBesselJ{2n}@{z}\assLegendreP[]{2n}@{\cos@@{\alpha}}</math>]] || <code>Error</code> || <code>BesselJ[0, z*Sin[\[Alpha]]] == Sum[(4*n + 1)*Divide[(2*n)!,(2)^(2*n)*((n)!)^(2)]*SphericalBesselJ[2*n, z]*LegendreP[2*n, 0, 3, Cos[\[Alpha]]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><code>{Plus[Complex[0.8683151459050518, -0.20203213835937428], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.0707372016677029], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Plus[Complex[0.9708614168197589, -0.04904886793011446], Times[-1.0, NSum[Times[Power[2, Times[-2, n]], Plus[1, Times[4, n]], Power[Factorial[n], -2], Factorial[Times[2, n]], LegendreP[Times[2, n], 0.8775825618903728], SphericalBesselJ[Times[2, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E11 10.60.E11] || [[Item:Q3786|<math>\sum_{n=0}^{\infty}\sphBesselJ{n}^{2}@{z} = \frac{\sinint@{2z}}{2z}</math>]] || <code>Error</code> || <code>Sum[(SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[SinIntegral[2*z],2*z]</code> || Missing Macro Error || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/10.60.E11 10.60.E11] || [[Item:Q3786|<math>\sum_{n=0}^{\infty}\sphBesselJ{n}^{2}@{z} = \frac{\sinint@{2z}}{2z}</math>]] || <code>Error</code> || <code>Sum[(SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[SinIntegral[2*z],2*z]</code> || Error || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/10.60.E12 10.60.E12] || [[Item:Q3787|<math>\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}^{2}@{z} = 1</math>]] || <code>Error</code> || <code>Sum[(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == 1</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E12 10.60.E12] || [[Item:Q3787|<math>\sum_{n=0}^{\infty}(2n+1)\sphBesselJ{n}^{2}@{z} = 1</math>]] || <code>Error</code> || <code>Sum[(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == 1</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[-1.0, NSum[Times[Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E13 10.60.E13] || [[Item:Q3788|<math>\sum_{n=0}^{\infty}(-1)^{n}(2n+1)\sphBesselJ{n}^{2}@{z} = \frac{\sin@{2z}}{2z}</math>]] || <code>Error</code> || <code>Sum[(- 1)^(n)*(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[Sin[2*z],2*z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.6123335037567501, 0.46246896224791606], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-1.2536290109103816, -0.6921871649112455], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.60.E13 10.60.E13] || [[Item:Q3788|<math>\sum_{n=0}^{\infty}(-1)^{n}(2n+1)\sphBesselJ{n}^{2}@{z} = \frac{\sin@{2z}}{2z}</math>]] || <code>Error</code> || <code>Sum[(- 1)^(n)*(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[Sin[2*z],2*z]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.6123335037567501, 0.46246896224791606], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-1.2536290109103816, -0.6921871649112455], NSum[Times[Power[-1, n], Plus[1, Times[2, n]], Power[SphericalBesselJ[n, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], 2]] <- {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.60.E14 10.60.E14] || [[Item:Q3789|<math>\sum_{n=0}^{\infty}(2n+1)(\sphBesselJ{n}'@{z})^{2} = \tfrac{1}{3}</math>]] || <code>Error</code> || <code>Sum[(2*n + 1)*(D[SphericalBesselJ[n, z], {z, 1}])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[1,3]</code> || Missing Macro Error || Aborted || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.61.E1 10.61.E1] || [[Item:Q3790|<math>\Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \BesselJ{\nu}@{xe^{3\pi i/4}}</math>]] || <code>KelvinBer(nu, x)+ I*KelvinBei(nu, x) = BesselJ(nu, x*exp(3*Pi*I/ 4))</code> || <code>KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x] == BesselJ[\[Nu], x*Exp[3*Pi*I/ 4]]</code> || Successful || Failure || Skip - symbolical successful subtest || Successful [Tested: 30]
@@ Line 413: / Line 439: @@
 | [https://dlmf.nist.gov/10.63.E7 10.63.E7] || [[Item:Q3828|<math>p_{\nu}s_{\nu} = r_{\nu}^{2}+q_{\nu}^{2}</math>]] || <code>p[nu]*s[nu] = (r[nu])^(2)+ (q[nu])^(2)</code> || <code>Subscript[p, \[Nu]]*Subscript[s, \[Nu]] == (Subscript[r, \[Nu]])^(2)+ (Subscript[q, \[Nu]])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/10.64.E1 10.64.E1] || [[Item:Q3829|<math>\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}</math>]] || <code>KelvinBer(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi)</code> || <code>KelvinBer[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 9] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.64.E1 10.64.E1] || [[Item:Q3829|<math>\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}</math>]] || <code>KelvinBer(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi)</code> || <code>KelvinBer[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.64.E2 10.64.E2] || [[Item:Q3830|<math>\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}</math>]] || <code>KelvinBei(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi)</code> || <code>KelvinBei[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 9] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.64.E2 10.64.E2] || [[Item:Q3830|<math>\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}</math>]] || <code>KelvinBei(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi)</code> || <code>KelvinBei[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.65#Ex1 10.65#Ex1] || [[Item:Q3831|<math>\Kelvinber{\nu}@@{x} = (\tfrac{1}{2}x)^{\nu}\sum_{k=0}^{\infty}\frac{\cos@{\frac{3}{4}\nu\pi+\frac{1}{2}k\pi}}{k!\EulerGamma@{\nu+k+1}}(\tfrac{1}{4}x^{2})^{k}</math>]] || <code>KelvinBer(nu, x) = ((1)/(2)*x)^(nu)* sum((cos((3)/(4)*nu*Pi +(1)/(2)*k*Pi))/(factorial(k)*GAMMA(nu + k + 1))*((1)/(4)*(x)^(2))^(k), k = 0..infinity)</code> || <code>KelvinBer[\[Nu], x] == (Divide[1,2]*x)^\[Nu]* Sum[Divide[Cos[Divide[3,4]*\[Nu]*Pi +Divide[1,2]*k*Pi],(k)!*Gamma[\[Nu]+ k + 1]]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
@@ Line 424: / Line 450: @@
 |-
 | [https://dlmf.nist.gov/10.65#Ex4 10.65#Ex4] || [[Item:Q3834|<math>\Kelvinbei{}@@{x} = \tfrac{1}{4}x^{2}-\frac{(\frac{1}{4}x^{2})^{3}}{(3!)^{2}}+\frac{(\frac{1}{4}x^{2})^{5}}{(5!)^{2}}-\dotsi</math>]] || <code>KelvinBei(, x) = (1)/(4)*(x)^(2)-(((1)/(4)*(x)^(2))^(3))/((factorial(3))^(2))+(((1)/(4)*(x)^(2))^(5))/((factorial(5))^(2))- ..</code> || <code>KelvinBei[, x] == Divide[1,4]*(x)^(2)-Divide[(Divide[1,4]*(x)^(2))^(3),((3)!)^(2)]+Divide[(Divide[1,4]*(x)^(2))^(5),((5)!)^(2)]- \[Ellipsis]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[-0.5575600630044937, …, KelvinBei[Null, 1.5]] <- {Rule[x, 1.5]}</code><br><code>Plus[-0.06249321838219961, …, KelvinBei[Null, 0.5]] <- {Rule[x, 0.5]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.65.E3 10.65.E3] || [[Item:Q3835|<math>\Kelvinker{n}@@{x} = \tfrac{1}{2}(\tfrac{1}{2}x)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\cos@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}-\ln@{\tfrac{1}{2}x}\Kelvinber{n}@@{x}+\tfrac{1}{4}\pi\Kelvinbei{n}@@{x}+\tfrac{1}{2}(\tfrac{1}{2}x)^{n}\sum_{k=0}^{\infty}\frac{\digamma@{k+1}+\digamma@{n+k+1}}{k!(n+k)!}\cos@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}</math>]] || <code>KelvinKer(n, x) = (1)/(2)*((1)/(2)*x)^(- n)* sum((factorial(n - k - 1))/(factorial(k))*cos((3)/(4)*n*Pi +(1)/(2)*k*Pi)*((1)/(4)*(x)^(2))^(k), k = 0..n - 1)- ln((1)/(2)*x)*KelvinBer(n, x)+(1)/(4)*Pi*KelvinBei(n, x)+(1)/(2)*((1)/(2)*x)^(n)* sum((Psi(k + 1)+ Psi(n + k + 1))/(factorial(k)*factorial(n + k))*cos((3)/(4)*n*Pi +(1)/(2)*k*Pi)*((1)/(4)*(x)^(2))^(k), k = 0..infinity)</code> || <code>KelvinKer[n, x] == Divide[1,2]*(Divide[1,2]*x)^(- n)* Sum[Divide[(n - k - 1)!,(k)!]*Cos[Divide[3,4]*n*Pi +Divide[1,2]*k*Pi]*(Divide[1,4]*(x)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]- Log[Divide[1,2]*x]*KelvinBer[n, x]+Divide[1,4]*Pi*KelvinBei[n, x]+Divide[1,2]*(Divide[1,2]*x)^(n)* Sum[Divide[PolyGamma[k + 1]+ PolyGamma[n + k + 1],(k)!*(n + k)!]*Cos[Divide[3,4]*n*Pi +Divide[1,2]*k*Pi]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Aborted || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[n, 1], Rule[x, 1.5]}</code><br><code>Indeterminate <- {Rule[n, 2], Rule[x, 1.5]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.65.E4 10.65.E4] || [[Item:Q3836|<math>\Kelvinkei{n}@@{x} = -\tfrac{1}{2}(\tfrac{1}{2}x)^{-n}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\sin@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}-\ln@{\tfrac{1}{2}x}\Kelvinbei{n}@@{x}-\tfrac{1}{4}\pi\Kelvinber{n}@@{x}+\tfrac{1}{2}(\tfrac{1}{2}x)^{n}\sum_{k=0}^{\infty}\frac{\digamma@{k+1}+\digamma@{n+k+1}}{k!(n+k)!}\sin@{\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi}(\tfrac{1}{4}x^{2})^{k}</math>]] || <code>KelvinKei(n, x) = -(1)/(2)*((1)/(2)*x)^(- n)* sum((factorial(n - k - 1))/(factorial(k))*sin((3)/(4)*n*Pi +(1)/(2)*k*Pi)*((1)/(4)*(x)^(2))^(k), k = 0..n - 1)- ln((1)/(2)*x)*KelvinBei(n, x)-(1)/(4)*Pi*KelvinBer(n, x)+(1)/(2)*((1)/(2)*x)^(n)* sum((Psi(k + 1)+ Psi(n + k + 1))/(factorial(k)*factorial(n + k))*sin((3)/(4)*n*Pi +(1)/(2)*k*Pi)*((1)/(4)*(x)^(2))^(k), k = 0..infinity)</code> || <code>KelvinKei[n, x] == -Divide[1,2]*(Divide[1,2]*x)^(- n)* Sum[Divide[(n - k - 1)!,(k)!]*Sin[Divide[3,4]*n*Pi +Divide[1,2]*k*Pi]*(Divide[1,4]*(x)^(2))^(k), {k, 0, n - 1}, GenerateConditions->None]- Log[Divide[1,2]*x]*KelvinBei[n, x]-Divide[1,4]*Pi*KelvinBer[n, x]+Divide[1,2]*(Divide[1,2]*x)^(n)* Sum[Divide[PolyGamma[k + 1]+ PolyGamma[n + k + 1],(k)!*(n + k)!]*Sin[Divide[3,4]*n*Pi +Divide[1,2]*k*Pi]*(Divide[1,4]*(x)^(2))^(k), {k, 0, Infinity}, GenerateConditions->None]</code> || Aborted || Aborted || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[n, 1], Rule[x, 1.5]}</code><br><code>Indeterminate <- {Rule[n, 2], Rule[x, 1.5]}</code><br></div></div>
+|-
+| [https://dlmf.nist.gov/10.65#Ex5 10.65#Ex5] || [[Item:Q3837|<math>\Kelvinker{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinber{}@@{x}+\tfrac{1}{4}\pi\Kelvinbei{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+1}}{((2k)!)^{2}}(\tfrac{1}{4}x^{2})^{2k}</math>]] || <code>KelvinBei(, x)+ sum((- 1)^(k)*(Psi(2*k + 1))/((factorial(2*k))^(2))*((1)/(4)*(x)^(2))^(2*k), k = 0..infinity)</code> || <code>KelvinBei[, x]+ Sum[(- 1)^(k)*Divide[PolyGamma[2*k + 1],((2*k)!)^(2)]*(Divide[1,4]*(x)^(2))^(2*k), {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Aborted || - || Skipped - Because timed out
 |-
 | [https://dlmf.nist.gov/10.65#Ex6 10.65#Ex6] || [[Item:Q3838|<math>\Kelvinkei{}@@{x} = -\ln@{\tfrac{1}{2}x}\Kelvinbei{}@@{x}-\tfrac{1}{4}\pi\Kelvinber{}@@{x}+\sum_{k=0}^{\infty}(-1)^{k}\frac{\digamma@{2k+2}}{((2k+1)!)^{2}}(\tfrac{1}{4}x^{2})^{2k+1}</math>]] || <code>KelvinBer(, x)+ sum((- 1)^(k)*(Psi(2*k + 2))/((factorial(2*k + 1))^(2))*((1)/(4)*(x)^(2))^(2*k + 1), k = 0..infinity)</code> || <code>KelvinBer[, x]+ Sum[(- 1)^(k)*Divide[PolyGamma[2*k + 2],((2*k + 1)!)^(2)]*(Divide[1,4]*(x)^(2))^(2*k + 1), {k, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Plus[-0.23161280473545226, Times[-1.0, KelvinBer[Null, 1.5]], KelvinKei[Null, 1.5]] <- {Rule[x, 1.5]}</code><br><code>Plus[-0.02641550246351669, Times[-1.0, KelvinBer[Null, 0.5]], KelvinKei[Null, 0.5]] <- {Rule[x, 0.5]}</code><br></div></div>
@@ Line 435: / Line 467: @@
 | [https://dlmf.nist.gov/10.65.E9 10.65.E9] || [[Item:Q3842|<math>\left(\Kelvinber{\nu}'@@{x}\right)^{2}+\left(\Kelvinbei{\nu}'@@{x}\right)^{2} = (\tfrac{1}{2}x)^{2\nu-2}\sum_{k=0}^{\infty}\frac{2k^{2}+2\nu k+\frac{1}{4}\nu^{2}}{\EulerGamma@{\nu+k+1}\EulerGamma@{\nu+2k+1}}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}</math>]] || <code>(diff( KelvinBer(nu, x), x$(1) ))^(2)+(diff( KelvinBei(nu, x), x$(1) ))^(2) = ((1)/(2)*x)^(2*nu - 2)* sum((2*(k)^(2)+ 2*nu*k +(1)/(4)*(nu)^(2))/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 1))*(((1)/(4)*(x)^(2))^(2*k))/(factorial(k)), k = 0..infinity)</code> || <code>(D[KelvinBer[\[Nu], x], {x, 1}])^(2)+(D[KelvinBei[\[Nu], x], {x, 1}])^(2) == (Divide[1,2]*x)^(2*\[Nu]- 2)* Sum[Divide[2*(k)^(2)+ 2*\[Nu]*k +Divide[1,4]*\[Nu]^(2),Gamma[\[Nu]+ k + 1]*Gamma[\[Nu]+ 2*k + 1]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 30]<div class="mw-collapsible-content"><code>3/30]: [[Float(undefined)+Float(undefined)*I <- {nu = -2, x = 3/2}</code><br><code>Float(undefined)+Float(undefined)*I <- {nu = -2, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 30]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[x, 1.5], Rule[ν, -2]}</code><br><code>Indeterminate <- {Rule[x, 0.5], Rule[ν, -2]}</code><br></div></div>
 |-
-| [https://dlmf.nist.gov/10.66.E1 10.66.E1] || [[Item:Q3843|<math>\Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!}</math>]] || <code>KelvinBer(nu, x)+ I*KelvinBei(nu, x) = sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)</code> || <code>KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x] == Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.12257968900025018, 0.2735107661041647], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.3467793075651209, -0.08562995402477025], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.66.E1 10.66.E1] || [[Item:Q3843|<math>\Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!}</math>]] || <code>KelvinBer(nu, x)+ I*KelvinBei(nu, x) = sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)</code> || <code>KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x] == Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.12257968900025018, 0.2735107661041647], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.3467793075651209, -0.08562995402477025], Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><</div></div>
 |-
-| [https://dlmf.nist.gov/10.66.E1 10.66.E1] || [[Item:Q3843|<math>\sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}\modBesselI{\nu+k}@{x}}{2^{k/2}k!}</math>]] || <code>sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) = sum((exp((3*nu + 3*k)* Pi*I/ 4)*(x)^(k)* BesselI(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)</code> || <code>Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None] == Sum[Divide[Exp[(3*\[Nu]+ 3*k)* Pi*I/ 4]*(x)^(k)* BesselI[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, k]], Pi]], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Times[3, k]], Pi]], BesselI[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], k], 1.5], Power[Factorial[k], -1]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+| [https://dlmf.nist.gov/10.66.E1 10.66.E1] || [[Item:Q3843|<math>\sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}\BesselJ{\nu+k}@{x}}{2^{k/2}k!} = \sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}\modBesselI{\nu+k}@{x}}{2^{k/2}k!}</math>]] || <code>sum((exp((3*nu + k)* Pi*I/ 4)*(x)^(k)* BesselJ(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity) = sum((exp((3*nu + 3*k)* Pi*I/ 4)*(x)^(k)* BesselI(nu + k, x))/((2)^(k/ 2)* factorial(k)), k = 0..infinity)</code> || <code>Sum[Divide[Exp[(3*\[Nu]+ k)* Pi*I/ 4]*(x)^(k)* BesselJ[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None] == Sum[Divide[Exp[(3*\[Nu]+ 3*k)* Pi*I/ 4]*(x)^(k)* BesselI[\[Nu]+ k, x],(2)^(k/ 2)* (k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[3, k]], Pi]], BesselI[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], k], Pi]], BesselJ[Plus[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], k], 1.5], Power[Factorial[k], -1]], {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Times[-1.0, NSum[Times[Power[1.5, k], Power[2, Times[Rational[-1, 2], k]], Power[E, Times[Complex[0, Rational[1, 4]], Plus[Times[3, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Times[</div></div>
 |-
-| [https://dlmf.nist.gov/10.66#Ex1 10.66#Ex1] || [[Item:Q3844|<math>\Kelvinber{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k}@{x}\modBesselI{2k}@{x}</math>]] || <code>KelvinBer(n, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k, x)*BesselI(2*k, x), k = - infinity..infinity)</code> || <code>KelvinBer[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k, x]*BesselI[2*k, x], {k, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 9] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.66#Ex1 10.66#Ex1] || [[Item:Q3844|<math>\Kelvinber{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k}@{x}\modBesselI{2k}@{x}</math>]] || <code>KelvinBer(n, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k, x)*BesselI(2*k, x), k = - infinity..infinity)</code> || <code>KelvinBer[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k, x]*BesselI[2*k, x], {k, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.66#Ex2 10.66#Ex2] || [[Item:Q3845|<math>\Kelvinbei{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k+1}@{x}\modBesselI{2k+1}@{x}</math>]] || <code>KelvinBei(n, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k + 1, x)*BesselI(2*k + 1, x), k = - infinity..infinity)</code> || <code>KelvinBei[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k + 1, x]*BesselI[2*k + 1, x], {k, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Error || Successful [Tested: 9] || Skipped - Because timed out
+| [https://dlmf.nist.gov/10.66#Ex2 10.66#Ex2] || [[Item:Q3845|<math>\Kelvinbei{n}@{x\sqrt{2}} = \sum_{k=-\infty}^{\infty}(-1)^{n+k}\BesselJ{n+2k+1}@{x}\modBesselI{2k+1}@{x}</math>]] || <code>KelvinBei(n, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k + 1, x)*BesselI(2*k + 1, x), k = - infinity..infinity)</code> || <code>KelvinBei[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k + 1, x]*BesselI[2*k + 1, x], {k, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/10.68#Ex5 10.68#Ex5] || [[Item:Q3868|<math>\HankelmodM{\nu}@{x} = (\Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x})^{\ifrac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2))^(Divide[1,2])</code> || Error || Successful || - || Successful [Tested: 30]
+| [https://dlmf.nist.gov/10.68#Ex5 10.68#Ex5] || [[Item:Q3868|<math>\HankelmodM{\nu}@{x} = (\Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x})^{\ifrac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2))^(Divide[1,2])</code> || Missing Macro Error || Successful || - || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/10.68#Ex6 10.68#Ex6] || [[Item:Q3869|<math>\HankelmodderivN{\nu}@{x} = (\Kelvinker{\nu}^{2}@@{x}+\Kelvinkei{\nu}^{2}@@{x})^{\ifrac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((KelvinKer[\[Nu], x])^(2)+ (KelvinKei[\[Nu], x])^(2))^(Divide[1,2])</code> || Error || Successful || - || Successful [Tested: 30]
+| [https://dlmf.nist.gov/10.68#Ex6 10.68#Ex6] || [[Item:Q3869|<math>\HankelmodderivN{\nu}@{x} = (\Kelvinker{\nu}^{2}@@{x}+\Kelvinkei{\nu}^{2}@@{x})^{\ifrac{1}{2}}</math>]] || <code>Error</code> || <code>Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((KelvinKer[\[Nu], x])^(2)+ (KelvinKei[\[Nu], x])^(2))^(Divide[1,2])</code> || Missing Macro Error || Successful || - || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/10.68#Ex9 10.68#Ex9] || [[Item:Q3872|<math>\HankelmodM{-n}@{x} = \HankelmodM{n}@{x}</math>]] || <code>Error</code> || <code>Sqrt[KelvinBer[- n, x]^2 + KelvinBei[- n, x]^2] == Sqrt[KelvinBer[n, x]^2 + KelvinBei[n, x]^2]</code> || Error || Failure || - || Successful [Tested: 9]
+| [https://dlmf.nist.gov/10.68#Ex9 10.68#Ex9] || [[Item:Q3872|<math>\HankelmodM{-n}@{x} = \HankelmodM{n}@{x}</math>]] || <code>Error</code> || <code>Sqrt[KelvinBer[- n, x]^2 + KelvinBei[- n, x]^2] == Sqrt[KelvinBer[n, x]^2 + KelvinBei[n, x]^2]</code> || Missing Macro Error || Failure || - || Successful [Tested: 9]
 |-
-| [https://dlmf.nist.gov/10.68#Ex17 10.68#Ex17] || [[Item:Q3884|<math>\HankelmodderivN{-\nu}@{x} = \HankelmodderivN{\nu}@{x}</math>]] || <code>Error</code> || <code>Sqrt[KelvinKer[- \[Nu], x]^2 + KelvinKei[- \[Nu], x]^2] == Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]</code> || Error || Failure || - || Successful [Tested: 30]
+| [https://dlmf.nist.gov/10.68#Ex17 10.68#Ex17] || [[Item:Q3884|<math>\HankelmodderivN{-\nu}@{x} = \HankelmodderivN{\nu}@{x}</math>]] || <code>Error</code> || <code>Sqrt[KelvinKer[- \[Nu], x]^2 + KelvinKei[- \[Nu], x]^2] == Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]</code> || Missing Macro Error || Failure || - || Successful [Tested: 30]
 |-
 | [https://dlmf.nist.gov/10.71.E1 10.71.E1] || [[Item:Q3902|<math>\int x^{1+\nu}f_{\nu}\diff{x} = -\frac{x^{1+\nu}}{\sqrt{2}}(f_{\nu+1}-g_{\nu+1})</math>]] || <code>int((x)^(1 + nu)* f[nu], x) = -((x)^(1 + nu))/(sqrt(2))*(f[nu + 1]- g[nu + 1])</code> || <code>Integrate[(x)^(1 + \[Nu])* Subscript[f, \[Nu]], x, GenerateConditions->None] == -Divide[(x)^(1 + \[Nu]),Sqrt[2]]*(Subscript[f, \[Nu]+ 1]- Subscript[g, \[Nu]+ 1])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.9346151411+.5776724966*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[1+nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = 1/2*3^(1/2)+1/2*I}</code><br><code>3.061934630+.4518721345*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[1+nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.9346151408625077, 0.5776724967688012] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[3.061934629891139, 0.45187213490403344] <- {Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, ν], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, Plus[1, ν]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, Plus[1, ν]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
@@ Line 459: / Line 491: @@
 | [https://dlmf.nist.gov/10.71.E7 10.71.E7] || [[Item:Q3908|<math>\int x(f_{\nu}^{2}-g_{\nu}^{2})\diff{x} = \tfrac{1}{2}x^{2}\left(f_{\nu}^{2}-f_{\nu-1}f_{\nu+1}-g_{\nu}^{2}+g_{\nu-1}g_{\nu+1}\right)</math>]] || <code>int(x*(f(f[nu])^(2)- g(g[nu])^(2)), x) = (f(f[nu])^(2)- f[nu - 1]*f[nu + 1]- g(g[nu])^(2)+ g[nu - 1]*g[nu + 1])</code> || <code>Integrate[x*(f(Subscript[f, \[Nu]])^(2)- g(Subscript[g, \[Nu]])^(2)), x, GenerateConditions->None] == (f(Subscript[f, \[Nu]])^(2)- Subscript[f, \[Nu]- 1]*Subscript[f, \[Nu]+ 1]- g(Subscript[g, \[Nu]])^(2)+ Subscript[g, \[Nu]- 1]*Subscript[g, \[Nu]+ 1])</code> || Failure || Failure || Error || Error
 |-
-| [https://dlmf.nist.gov/10.71#Ex1 10.71#Ex1] || [[Item:Q3909|<math>\int x\HankelmodM{\nu}^{2}@{x}\diff{x} = x(\Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x})</math>]] || <code>Error</code> || <code>Integrate[x*(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x*(KelvinBer[\[Nu], x]*D[KelvinBei[\[Nu], x], {x, 1}]- D[KelvinBer[\[Nu], x], {x, 1}]*KelvinBei[\[Nu], x])</code> || Error || Successful || - || Successful [Tested: 30]
+| [https://dlmf.nist.gov/10.71#Ex1 10.71#Ex1] || [[Item:Q3909|<math>\int x\HankelmodM{\nu}^{2}@{x}\diff{x} = x(\Kelvinber{\nu}@@{x}\Kelvinbei{\nu}'@@{x}-\Kelvinber{\nu}'@@{x}\Kelvinbei{\nu}@@{x})</math>]] || <code>Error</code> || <code>Integrate[x*(Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x*(KelvinBer[\[Nu], x]*D[KelvinBei[\[Nu], x], {x, 1}]- D[KelvinBer[\[Nu], x], {x, 1}]*KelvinBei[\[Nu], x])</code> || Missing Macro Error || Successful || - || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/10.71#Ex2 10.71#Ex2] || [[Item:Q3910|<math>\int x\HankelmodderivN{\nu}^{2}@{x}\diff{x} = x(\Kelvinker{\nu}@@{x}\Kelvinkei{\nu}'@@{x}-\Kelvinker{\nu}'@@{x}\Kelvinkei{\nu}@@{x})</math>]] || <code>Error</code> || <code>Integrate[x*(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x*(KelvinKer[\[Nu], x]*D[KelvinKei[\[Nu], x], {x, 1}]- D[KelvinKer[\[Nu], x], {x, 1}]*KelvinKei[\[Nu], x])</code> || Error || Successful || - || Successful [Tested: 30]
+| [https://dlmf.nist.gov/10.71#Ex2 10.71#Ex2] || [[Item:Q3910|<math>\int x\HankelmodderivN{\nu}^{2}@{x}\diff{x} = x(\Kelvinker{\nu}@@{x}\Kelvinkei{\nu}'@@{x}-\Kelvinker{\nu}'@@{x}\Kelvinkei{\nu}@@{x})</math>]] || <code>Error</code> || <code>Integrate[x*(Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2])^(2), x, GenerateConditions->None] == x*(KelvinKer[\[Nu], x]*D[KelvinKei[\[Nu], x], {x, 1}]- D[KelvinKer[\[Nu], x], {x, 1}]*KelvinKei[\[Nu], x])</code> || Missing Macro Error || Successful || - || Successful [Tested: 30]
 |-
 | [https://dlmf.nist.gov/10.73.E1 10.73.E1] || [[Item:Q3912|<math>\frac{1}{r}\pderiv{}{r}\left(r\pderiv{V}{r}\right)+\frac{1}{r^{2}}\pderiv[2]{V}{\phi}+\pderiv[2]{V}{z} = 0</math>]] || <code>(1)/(r)*diff((r*diff(V, r))+(1)/((r)^(2))*diff(V, [phi$(2)]), r)+ diff(V, [z$(2)]) = 0</code> || <code>Divide[1,r]*D[(r*D[V, r])+Divide[1,(r)^(2)]*D[V, {\[Phi], 2}], r]+ D[V, {z, 2}] == 0</code> || Successful || Successful || - || Successful [Tested: 300]
 |-
 |}

Results of Bessel Functions II: Difference between revisions

Revision as of 19:52, 15 October 2020

Navigation menu

Search