Hypergeometric Function - 15.14 Integrals

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
15.14.E1	${\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}\mathbf{F}\left({a,b\atop c};-x\right)\mathrm{d}x=\frac{\Gamma\left(s\right)\Gamma\left(a-s\right)\Gamma\left(b-s\right)}{\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-s\right)}}}$ \int_{0}^{\infty}x^{s-1}\hyperOlverF@@{a}{b}{c}{-x}\diff{x} = \frac{\EulerGamma@{s}\EulerGamma@{a-s}\EulerGamma@{b-s}}{\EulerGamma@{a}\EulerGamma@{b}\EulerGamma@{c-s}}	${\displaystyle{\displaystyle\min(\Re a>\Re s,\Re b)>\Re s,\Re s>0,\Re(a-s)>0,\Re(b-s)>0,\Re a>0,\Re b>0,\Re(c-s)>0,|(-x)|<1,\Re(c+s)>0}}$	int((x)^(s - 1)* hypergeom([a, b], [c], - x)/GAMMA(c), x = 0..infinity) = (GAMMA(s)*GAMMA(a - s)*GAMMA(b - s))/(GAMMA(a)*GAMMA(b)*GAMMA(c - s))	Integrate[(x)^(s - 1)* Hypergeometric2F1Regularized[a, b, c, - x], {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[s]*Gamma[a - s]*Gamma[b - s],Gamma[a]*Gamma[b]*Gamma[c - s]]	Successful	Aborted	-	Skipped - Because timed out