Results of Bessel Functions II
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, z*exp(m*Pi*I)) = exp(m*nu*Pi*I)*BesselI(nu, z) |
BesselI[\[Nu], z*Exp[m*Pi*I]] == Exp[m*\[Nu]*Pi*I]*BesselI[\[Nu], z] |
Failure | Failure | Failed [132 / 210] 132/210]: [[-2.206479866-1.131319388*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.5147384726+.2724622562e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [120 / 210]
{Complex[-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, z*exp(m*Pi*I)) = exp(- m*nu*Pi*I)*BesselK(nu, z)- Pi*I*sin(m*nu*Pi)*csc(nu*Pi)*BesselI(nu, z) |
BesselK[\[Nu], z*Exp[m*Pi*I]] == Exp[- m*\[Nu]*Pi*I]*BesselK[\[Nu], z]- Pi*I*Sin[m*\[Nu]*Pi]*Csc[\[Nu]*Pi]*BesselI[\[Nu], z] |
Failure | Failure | Failed [170 / 210] 170/210]: [[2.965939338+3.157233720*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}-10.37113928-12.75980866*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2} |
Failed [162 / 210]
{Complex[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, z*exp(m*Pi*I)) = (I/ Pi)*(+ exp(m*nu*Pi*I)*BesselK(nu, z*exp(+ Pi*I))- exp((m - 1)* nu*Pi*I)*BesselK(nu, z)) |
BesselI[\[Nu], z*Exp[m*Pi*I]] == (I/ Pi)*(+ Exp[m*\[Nu]*Pi*I]*BesselK[\[Nu], z*Exp[+ Pi*I]]- Exp[(m - 1)* \[Nu]*Pi*I]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [152 / 210] 152/210]: [[-2.316975457-.8668337446*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.5132395470-.3232131754e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = (I/ Pi)*(- exp(m*nu*Pi*I)*BesselK(nu, z*exp(- Pi*I))+ exp((m + 1)* nu*Pi*I)*BesselK(nu, z)) |
BesselI[\[Nu], z*Exp[m*Pi*I]] == (I/ Pi)*(- Exp[m*\[Nu]*Pi*I]*BesselK[\[Nu], z*Exp[- Pi*I]]+ Exp[(m + 1)* \[Nu]*Pi*I]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [190 / 210] 190/210]: [[-2.206479866-1.131319388*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}.5147384726+.2724622561e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = csc(nu*Pi)*(+ sin(m*nu*Pi)*BesselK(nu, z*exp(+ Pi*I))- sin((m - 1)* nu*Pi)*BesselK(nu, z)) |
BesselK[\[Nu], z*Exp[m*Pi*I]] == Csc[\[Nu]*Pi]*(+ Sin[m*\[Nu]*Pi]*BesselK[\[Nu], z*Exp[+ Pi*I]]- Sin[(m - 1)* \[Nu]*Pi]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [158 / 210] 158/210]: [[-2.723238516+7.278993081*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}29.12762958-25.06220737*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = csc(nu*Pi)*(- sin(m*nu*Pi)*BesselK(nu, z*exp(- Pi*I))+ sin((m + 1)* nu*Pi)*BesselK(nu, z)) |
BesselK[\[Nu], z*Exp[m*Pi*I]] == Csc[\[Nu]*Pi]*(- Sin[m*\[Nu]*Pi]*BesselK[\[Nu], z*Exp[- Pi*I]]+ Sin[(m + 1)* \[Nu]*Pi]*BesselK[\[Nu], z]) |
Failure | Failure | Failed [170 / 210] 170/210]: [[2.965939338+3.157233717*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}-10.37113929-12.75980866*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = (- 1)^(m*n)* BesselK(n, z)+(- 1)^(n*(m - 1)- 1)* m*Pi*I*BesselI(n, z) |
BesselK[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)* BesselK[n, z]+(- 1)^(n*(m - 1)- 1)* m*Pi*I*BesselI[n, z] |
Failure | Failure | Failed [57 / 63] 57/63]: [[-1.971501919+2.706233555*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}-.7368261646+.3579119854*I <- {z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = +(- 1)^(n*(m - 1))* m*BesselK(n, z*exp(+ Pi*I))-(- 1)^(n*m)*(m - 1)* BesselK(n, z) |
BesselK[n, z*Exp[m*Pi*I]] == +(- 1)^(n*(m - 1))* m*BesselK[n, z*Exp[+ Pi*I]]-(- 1)^(n*m)*(m - 1)* BesselK[n, z] |
Failure | Failure | Failed [51 / 63] 51/63]: [[-1.971501920+2.706233556*I <- {z = 1/2*3^(1/2)+1/2*I, m = 2, n = 1}.7368261602-.357911988*I <- {z = 1/2*3^(1/2)+1/2*I, 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, z*exp(m*Pi*I)) = -(- 1)^(n*(m - 1))* m*BesselK(n, z*exp(- Pi*I))+(- 1)^(n*m)*(m + 1)* BesselK(n, z) |
BesselK[n, z*Exp[m*Pi*I]] == -(- 1)^(n*(m - 1))* m*BesselK[n, z*Exp[- Pi*I]]+(- 1)^(n*m)*(m + 1)* BesselK[n, z] |
Failure | Failure | Failed [54 / 63] 54/63]: [[-1.971501919+2.706233556*I <- {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}-.7368261645+.357911985*I <- {z = 1/2*3^(1/2)+1/2*I, 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+.1347267497*I <- {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}.8978926857-1.555608423*I <- {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(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(z*cos(theta)) = BesselI(0, z)+ 2*sum(BesselI(k, z)*cos(k*theta), k = 1..infinity) |
Exp[z*Cos[\[Theta]]] == BesselI[0, z]+ 2*Sum[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(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) |
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] |
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)- 2*BesselI(2, z)+ 2*BesselI(4, z)- 2*BesselI(6, z)+ .. |
1 == BesselI[0, z]- 2*BesselI[2, z]+ 2*BesselI[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)+ 2*BesselI(1, z)+ 2*BesselI(2, z)+ 2*BesselI(3, z)+ .. |
Exp[+ z] == BesselI[0, z]+ 2*BesselI[1, z]+ 2*BesselI[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)- 2*BesselI(1, z)+ 2*BesselI(2, z)- 2*BesselI(3, z)+ .. |
Exp[- z] == BesselI[0, z]- 2*BesselI[1, z]+ 2*BesselI[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 = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}3.110500858 < 3.110500858 <- {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(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)*Pi*csc(nu*Pi)*(diff(BesselI(- nu, z), nu)- diff(BesselI(nu, z), nu))- Pi*cot(nu*Pi)*BesselK(nu, z) |
D[BesselK[\[Nu], z], \[Nu]] == Divide[1,2]*Pi*Csc[\[Nu]*Pi]*(D[BesselI[- \[Nu], z], \[Nu]]- D[BesselI[\[Nu], z], \[Nu]])- Pi*Cot[\[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)/(Pi*z))^((1)/(2))* sinh(z) |
BesselI[Divide[1,2], z] == (Divide[2,Pi*z])^(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)/(Pi*z))^((1)/(2))* cosh(z) |
BesselI[-Divide[1,2], z] == (Divide[2,Pi*z])^(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)/(2*z))^((1)/(2))* exp(- z) |
BesselK[-Divide[1,2], z] == (Divide[Pi,2*z])^(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), 2*nu + 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-.3396157390*I <- {nu = -1/2, z = 1/2*3^(1/2)+1/2*I}-.4588638571-.5759587792*I <- {nu = -1/2, z = -1/2+1/2*I*3^(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), 2*nu + 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))*(2*z)^(nu)* exp(- z)*KummerU(nu +(1)/(2), 2*nu + 1, 2*z) |
BesselK[\[Nu], z] == (Pi)^(Divide[1,2])*(2*z)^\[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) = ((2*z)^(-(1)/(2))* WhittakerM(0, nu, 2*z))/((2)^(2*nu)* GAMMA(nu + 1)) |
BesselI[\[Nu], z] == Divide[(2*z)^(-Divide[1,2])* WhittakerM[0, \[Nu], 2*z],(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)/(2*z))^((1)/(2))* WhittakerW(0, nu, 2*z) |
BesselK[\[Nu], z] == (Divide[Pi,2*z])^(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)/(2*z))^((1)/(2))* exp(- z)*(sum((a[k]*(nu))/((z)^(k)), k = 0..ell - 1)+ R[ell]*(nu , z)) |
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)) |
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)* 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)) |
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)*(3*p - 5*(p)^(3)) |
Subscript[U, 1]*(p) == Divide[1,24]*(3*p - 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)*(- 9*p + 7*(p)^(3)) |
Subscript[V, 1]*(p) == Divide[1,24]*(- 9*p + 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)*(2*k + 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)*(2*k + 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)/(2*k)- ln((1)/(2)*x))*(((1)/(2)*x)^(2*k))/(2*k*(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[1,2*k]- Log[Divide[1,2]*x])*Divide[(Divide[1,2]*x)^(2*k),2*k*((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) = 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) |
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] |
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))/(2*nu + 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))/(2*nu + 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))/(2*nu - 1)*(BesselI(nu, x)- BesselI(nu - 1, x))-((2)^(- nu + 1))/((2*nu - 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))/(2*nu - 1)*(BesselI(nu, x)+ BesselI(nu - 1, x))+((2)^(- nu + 1))/((2*nu - 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))/(2*nu + 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))/(2*nu + 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))/(2*nu - 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)*Pi*sec((1)/(2)*Pi*nu) |
Integrate[BesselK[\[Nu], t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*Sec[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(a*t)*BesselK(0, t), t = 0..infinity) = (Pi)/(2*(1 + (a)^(2))^((1)/(2))) |
Integrate[Cos[a*t]*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(a*t)*BesselK(0, t), t = 0..infinity) = (arcsinh(a))/((1 + (a)^(2))^((1)/(2))) |
Integrate[Sin[a*t]*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, b*t)*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], 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)]] |
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, 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))) |
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)]] |
Failure | Aborted | Failed [228 / 300] 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}-.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} |
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, 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))) |
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)]] |
Failure | Aborted | Failed [144 / 288] 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}-.2830456904e-1-1.996429597*I <- {b = -3/2, nu = 1/2*3^(1/2)+1/2*I, 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, 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) |
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)]] |
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, 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)) |
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)] |
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(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))) |
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)]] |
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(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))) |
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)]] |
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 + 2*k)* GAMMA(nu + k))/(factorial(k))*BesselI(nu + 2*k, z), k = 0..infinity) |
(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] |
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)+ 2*sum((BesselI(2*k, z))/(k), k = 1..infinity) |
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] |
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 + 2*k)* BesselI(n + 2*k, 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 + 2*k)* BesselI[n + 2*k, 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)])+ x*diff(w, x)+((nu)^(2)- (x)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]+(\[Nu]^(2)- (x)^(2))* w == 0 |
Failure | Failure | Failed [240 / 300] 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}-.2165063507+.8750000006*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, 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(I*nu, 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(I*nu, 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$(2)])+ 2*z*diff(w, z)+((z)^(2)- n*(n + 1))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]+((z)^(2)- n*(n + 1))* w == 0 |
Failure | Failure | Failed [210 / 210] 210/210]: [[-1.732050808+.3733632160e-9*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}-5.196152424-2.000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2} |
Failed [210 / 210]
{Complex[-1.7320508075688772, 1.1102230246251565*^-16] <- {Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-5.196152422706633, -1.9999999999999996] <- {Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 10.47.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+2z\deriv{w}{z}-\left(z^{2}+n(n+1)\right)w = 0} | (z)^(2)* diff(w, [z$(2)])+ 2*z*diff(w, z)-((z)^(2)+ n*(n + 1))* w = 0 |
(z)^(2)* D[w, {z, 2}]+ 2*z*D[w, z]-((z)^(2)+ n*(n + 1))* w == 0 |
Failure | Failure | Failed [210 / 210] 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}-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} |
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)* I*sqrt((1)/(2)*Pi/ z)*HankelH1(- n -(1)/(2), z) |
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] |
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)* I*sqrt((1)/(2)*Pi/ z)*HankelH2(- n -(1)/(2), z) |
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] |
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, I*z] == -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]*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] |
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]*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] |
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[I*z]*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[- I*z]*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]*Pi*Exp[- 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]*Pi*Divide[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]*Pi*Exp[- 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]*Pi*Exp[- 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)^(2*k + 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] == - 2*I*(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] == (2*n + 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]*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] |
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) = ((2*n + 1)/ z)* f[n]*(z) |
Subscript[f, n - 1]*(z)+ Subscript[f, n + 1]*(z) == ((2*n + 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-.3660254033*I <- {z = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, f[n+m] = 1/2*3^(1/2)+1/2*I, n = 1, m = 3}.9999999993-.9999999984*I <- {z = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, f[n+m] = 1/2*3^(1/2)+1/2*I, 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) = ((2*n + 1)/ z)* g[n]*(z) |
Subscript[g, n - 1]*(z)- Subscript[g, n + 1]*(z) == ((2*n + 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+1.366025403*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}.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} |
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)!*(2*n + 2*k + 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[(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] |
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)!*(2*n + 2*k + 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[(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] |
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[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*n + 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[I*z*Cos[\[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[- z*t]*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),2*Pi]*Integrate[Exp[I*z*t]*LegendreQ[n, 0, 3, t], {t, I*Infinity, (- 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[I*z*t]*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[I*z*t]*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)- 2*z*t]],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)- 2*z*t]],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)+ 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] |
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)+ 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] |
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)+ 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] |
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]),((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] |
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[(2*n + 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[(2*n + 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[(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] |
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, 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] |
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, 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] |
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 /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] |
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[I*z*Cos[\[Alpha]]] == Sum[(2*n + 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[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] |
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[- 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] |
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, 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] |
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[2*z],2*z] |
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[(2*n + 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)*(2*n + 1)* (SphericalBesselJ[n, z])^(2), {n, 0, Infinity}, GenerateConditions->None] == Divide[Sin[2*z],2*z] |
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[(2*n + 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)+ I*KelvinBei(nu, x) = BesselJ(nu, x*exp(3*Pi*I/ 4)) |
KelvinBer[\[Nu], x]+ I*KelvinBei[\[Nu], x] == BesselJ[\[Nu], x*Exp[3*Pi*I/ 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, x*exp(3*Pi*I/ 4)) = exp(nu*Pi*I)*BesselJ(nu, x*exp(- Pi*I/ 4)) |
BesselJ[\[Nu], x*Exp[3*Pi*I/ 4]] == Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], x*Exp[- Pi*I/ 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(nu*Pi*I)*BesselJ(nu, x*exp(- Pi*I/ 4)) = exp(nu*Pi*I/ 2)*BesselI(nu, x*exp(Pi*I/ 4)) |
Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], x*Exp[- Pi*I/ 4]] == Exp[\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[Pi*I/ 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(nu*Pi*I/ 2)*BesselI(nu, x*exp(Pi*I/ 4)) = exp(3*nu*Pi*I/ 2)*BesselI(nu, x*exp(- 3*Pi*I/ 4)) |
Exp[\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[Pi*I/ 4]] == Exp[3*\[Nu]*Pi*I/ 2]*BesselI[\[Nu], x*Exp[- 3*Pi*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 \Kelvinker{\nu}@@{x}+i\Kelvinkei{\nu}@@{x} = e^{-\nu\pi i/2}\modBesselK{\nu}@{xe^{\pi i/4}}} | KelvinKer(nu, x)+ I*KelvinKei(nu, x) = exp(- nu*Pi*I/ 2)*BesselK(nu, x*exp(Pi*I/ 4)) |
KelvinKer[\[Nu], x]+ I*KelvinKei[\[Nu], x] == Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], x*Exp[Pi*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 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(- nu*Pi*I/ 2)*BesselK(nu, x*exp(Pi*I/ 4)) = (1)/(2)*Pi*I*HankelH1(nu, x*exp(3*Pi*I/ 4)) |
Exp[- \[Nu]*Pi*I/ 2]*BesselK[\[Nu], x*Exp[Pi*I/ 4]] == Divide[1,2]*Pi*I*HankelH1[\[Nu], x*Exp[3*Pi*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)*Pi*I*HankelH1(nu, x*exp(3*Pi*I/ 4)) = -(1)/(2)*Pi*I*exp(- nu*Pi*I)*HankelH2(nu, x*exp(- Pi*I/ 4)) |
Divide[1,2]*Pi*I*HankelH1[\[Nu], x*Exp[3*Pi*I/ 4]] == -Divide[1,2]*Pi*I*Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], x*Exp[- Pi*I/ 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)])+ x*diff(w, x)-(I*(x)^(2)+ (nu)^(2))* w = 0 |
(x)^(2)* D[w, {x, 2}]+ x*D[w, x]-(I*(x)^(2)+ \[Nu]^(2))* w == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[1.125000000-2.948557160*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 3/2}.1249999997-1.216506352*I <- {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [300 / 300]
{Complex[1.1249999999999996, -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)])- x*diff(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}]- x*D[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(nu*Pi)*KelvinBer(nu, x)+ sin(nu*Pi)*KelvinBei(nu, x)+(2/ Pi)* sin(nu*Pi)*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(nu*Pi)*KelvinBer(nu, x)+ cos(nu*Pi)*KelvinBei(nu, x)+(2/ Pi)* sin(nu*Pi)*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(nu*Pi)*KelvinKer(nu, x)- sin(nu*Pi)*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(nu*Pi)*KelvinKer(nu, x)+ cos(nu*Pi)*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), x*sqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*cos(x +(Pi)/(8))- exp(- x)*cos(x -(Pi)/(8))) |
KelvinBer[Divide[1,2], x*Sqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(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), x*sqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*sin(x +(Pi)/(8))+ exp(- x)*sin(x -(Pi)/(8))) |
KelvinBei[Divide[1,2], x*Sqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(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), x*sqrt(2)) = ((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*sin(x +(Pi)/(8))- exp(- x)*sin(x -(Pi)/(8))) |
KelvinBer[-Divide[1,2], x*Sqrt[2]] == Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(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), x*sqrt(2)) = -((2)^(-(3)/(4)))/(sqrt(Pi*x))*(exp(x)*cos(x +(Pi)/(8))+ exp(- x)*cos(x -(Pi)/(8))) |
KelvinBei[-Divide[1,2], x*Sqrt[2]] == -Divide[(2)^(-Divide[3,4]),Sqrt[Pi*x]]*(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), x*sqrt(2)) = KelvinKei(-(1)/(2), x*sqrt(2)) |
KelvinKer[Divide[1,2], x*Sqrt[2]] == KelvinKei[-Divide[1,2], x*Sqrt[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), x*sqrt(2)) = - (2)^(-(3)/(4))*sqrt((Pi)/(x))*exp(- x)*sin(x -(Pi)/(8)) |
KelvinKei[-Divide[1,2], x*Sqrt[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), x*sqrt(2)) = - KelvinKer(-(1)/(2), x*sqrt(2)) |
KelvinKei[Divide[1,2], x*Sqrt[2]] == - KelvinKer[-Divide[1,2], x*Sqrt[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), x*sqrt(2)) = - (2)^(-(3)/(4))*sqrt((Pi)/(x))*exp(- x)*cos(x -(Pi)/(8)) |
- KelvinKer[-Divide[1,2], x*Sqrt[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) = -(nu*sqrt(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]-(4*nu/ 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, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi) |
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] |
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, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi) |
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] |
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)*nu*Pi +(1)/(2)*k*Pi))/(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]*k*Pi],(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)*nu*Pi +(1)/(2)*k*Pi))/(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]*k*Pi],(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)*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) |
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] |
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)*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) |
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] |
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(2*k + 1))/((factorial(2*k))^(2))*((1)/(4)*(x)^(2))^(2*k), k = 0..infinity) |
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] |
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(2*k + 2))/((factorial(2*k + 1))^(2))*((1)/(4)*(x)^(2))^(2*k + 1), k = 0..infinity) |
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] |
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)^(2*nu)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 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]+ 2*k + 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)^(2*nu + 1)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k + 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]+ 2*k + 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-2*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}-.41528503e-2+.322695404e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, 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)^(2*nu - 1)* sum((1)/(GAMMA(nu + k + 1)*GAMMA(nu + 2*k))*(((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]+ 2*k]]*Divide[(Divide[1,4]*(x)^(2))^(2*k),(k)!], {k, 0, Infinity}, GenerateConditions->None] |
Failure | Successful | Failed [25 / 30] 25/30]: [[.71978298e-2-.3037583875e-1*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2}.607273780e-1-.1071579728*I <- {nu = 1/2*3^(1/2)+1/2*I, 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)^(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) |
(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] |
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)+ 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) |
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] |
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((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) |
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] |
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, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k, x)*BesselI(2*k, x), k = - infinity..infinity) |
KelvinBer[n, x*Sqrt[2]] == Sum[(- 1)^(n + k)* BesselJ[n + 2*k, 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, x*sqrt(2)) = sum((- 1)^(n + k)* BesselJ(n + 2*k + 1, x)*BesselI(2*k + 1, x), k = - infinity..infinity) |
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] |
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+.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}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)} |
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+.8580421171*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu-1] = 1/2*3^(1/2)+1/2*I}.30703090e-2+1.331056152*I <- {nu = 1/2*3^(1/2)+1/2*I, x = 3/2, f[nu] = 1/2*3^(1/2)+1/2*I, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu-1] = -1/2+1/2*I*3^(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(x*f[nu]*g[nu], x) = (1)/(4)*(x)^(2)*(2*f[nu]*g[nu]- f[nu - 1]*g[nu + 1]- f[nu + 1]*g[nu - 1]) |
Integrate[x*Subscript[f, \[Nu]]*Subscript[g, \[Nu]], x, GenerateConditions->None] == Divide[1,4]*(x)^(2)*(2*Subscript[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+.9742785795*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, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = 1/2*3^(1/2)+1/2*I, g[nu-1] = 1/2*3^(1/2)+1/2*I}-.2058892896+.7683892900*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, f[nu-1] = 1/2*3^(1/2)+1/2*I, g[nu] = 1/2*3^(1/2)+1/2*I, g[1+nu] = 1/2*3^(1/2)+1/2*I, g[nu-1] = -1/2+1/2*I*3^(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((r*diff(V, r))+(1)/((r)^(2))*diff(V, [phi$(2)]), r)+ diff(V, [z$(2)]) = 0 |
Divide[1,r]*D[(r*D[V, r])+Divide[1,(r)^(2)]*D[V, {\[Phi], 2}], r]+ D[V, {z, 2}] == 0 |
Successful | Successful | - | Successful [Tested: 300] |