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! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
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| [https://dlmf.nist.gov/18.35.E4 18.35.E4] || [[Item:Q6043|<math>\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}</syntaxhighlight> || <math>0 < \theta, \theta < \pi</math> || <syntaxhighlight lang=mathematica>(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]</syntaxhighlight> || Error || Successful || - || Successful [Tested: 300]
| [https://dlmf.nist.gov/18.35.E4 18.35.E4] || [[Item:Q6043|<math>\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}</syntaxhighlight> || <math>0 < \theta, \theta < \pi</math> || <syntaxhighlight lang=mathematica>(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]</syntaxhighlight> || Error || Successful || - || Successful [Tested: 300]
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{{Scrolling table/end}}
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/1.2.E6 1.2.E6] || [[Item:Q35|<math>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
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| [https://dlmf.nist.gov/1.2.E7 1.2.E7] || [[Item:Q36|<math>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
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| [https://dlmf.nist.gov/1.2.E8 1.2.E8] || [[Item:Q37|<math>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
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| [https://dlmf.nist.gov/1.2.E10 1.2.E10] || [[Item:Q39|<math>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)</syntaxhighlight> || <syntaxhighlight lang=mathematica>n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/1.2.E22 1.2.E22] || [[Item:Q51|<math>M(r) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M(r) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || [[Item:Q54|<math>M(1) = A</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M(1) = A</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>M(1) = ((a[1]+ a[2]+ .. + a[n])/(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n])</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || [[Item:Q55|<math>M(-1) = H</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>M(-1) = H</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>M(- 1) = H</syntaxhighlight> || <syntaxhighlight lang=mathematica>M[- 1] == H</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/1.2.E26 1.2.E26] || [[Item:Q56|<math>\lim_{r\to 0}M(r) = G</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\lim_{r\to 0}M(r) = G</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/1.4.E8 1.4.E8] || [[Item:Q87|<math>f^{(2)}(x) = \deriv[2]{f}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>f^{(2)}(x) = \deriv[2]{f}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(f(x))^(2) = diff(f, [x$(2)])</syntaxhighlight> || <syntaxhighlight lang=mathematica>(f[x])^(2) == D[f, {x, 2}]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7500000006+1.299038106*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2500000002+.4330127020*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.000000001+1.732050808*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7500000006-1.299038106*I
Test Values: {f = -1/2+1/2*I*3^(1/2), x = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7500000000000002, 1.299038105676658]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.25000000000000006, 0.4330127018922193]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/1.4.E8 1.4.E8] || [[Item:Q87|<math>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f, [x$(2)]) = diff(diff(f, x), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[f, {x, 2}] == D[D[f, x], x]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 30]
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| [https://dlmf.nist.gov/1.4.E9 1.4.E9] || [[Item:Q88|<math>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(f(x))^(n) = diff((f(x))^(n - 1), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(f[x])^(n) == D[(f[x])^(n - 1), x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [84 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .299038106+.7500000000*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1160254034+.7990381060*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4999999999+.6339745980*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5669872980+.2500000000*I
Test Values: {f = 1/2*3^(1/2)+1/2*I, x = .5, n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [84 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.299038105676658, 0.7499999999999999]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.11602540378443849, 0.799038105676658]
Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/1.4.E16 1.4.E16] || [[Item:Q95|<math>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(f*g, x) = (int(f, x))*g - int((int(f, x))*diff(g, x), x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[f*g, x, GenerateConditions->None] == (Integrate[f, x, GenerateConditions->None])*g - Integrate[(Integrate[f, x, GenerateConditions->None])*D[g, x], x, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 100]
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Revision as of 13:27, 18 May 2021

DLMF Formula Constraints Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
1.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}}
\binom{n}{k} = \frac{n!}{(n-k)!k!}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))

Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]
Successful Successful - Successful [Tested: 9]
18.35.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}}
\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \theta, \theta < \pi} 
(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)

Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]
Error Successful - Successful [Tested: 300]
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