test

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
1.2.E1	${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}=\frac{n!}{(n-k)!k!}}}$ \binom{n}{k} = \frac{n!}{(n-k)!k!}		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	${\displaystyle{\displaystyle\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n}}}{n!}e^{\mathrm{i}n\theta}\*{{}_{2}F_{1}}\left({-n,\lambda+\mathrm{i}\tau_{a,b}(\theta)\atop-n-\lambda+1+\mathrm{i}\tau_{a,b}(\theta)};e^{-2\mathrm{i}\theta}\right)=\sum_{\ell=0}^{n}\frac{{\left(\lambda+\mathrm{i}\tau_{a,b}(\theta)\right)_{\ell}}}{\ell!}\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n-\ell}}}{(n-\ell)!}e^{\mathrm{i}(n-2\ell)\theta}}}$ \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}	${\displaystyle{\displaystyle 0<\theta,\theta<\pi}}$	(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]