Hypergeometric Function - 15.15 Sums

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
15.15.E1	${\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};\frac{1}{z}\right)=\left(1-\frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*\mathbf{F}\left({-s,b\atop c};\frac{1}{z_{0}}\right)\left(1-\frac{z}{z_{0}}\right)^{-s}}}$ \hyperOlverF@@{a}{b}{c}{\frac{1}{z}} = \left(1-\frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*\hyperOlverF@@{-s}{b}{c}{\frac{1}{z_{0}}}\left(1-\frac{z}{z_{0}}\right)^{-s}		hypergeom([a, b], [c], (1)/(z))/GAMMA(c) = (1 -(z[0])/(z))^(- a)* sum((a[s])/(factorial(s))* hypergeom([- s, b], [c], (1)/(z[0]))/GAMMA(c)*(1 -(z)/(z[0]))^(- s), s = 0..infinity)	Hypergeometric2F1Regularized[a, b, c, Divide[1,z]] == (1 -Divide[Subscript[z, 0],z])^(- a)* Sum[Divide[Subscript[a, s],(s)!]* Hypergeometric2F1Regularized[- s, b, c, Divide[1,Subscript[z, 0]]]*(1 -Divide[z,Subscript[z, 0]])^(- s), {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out