Formula:KLS:01.06:02

<< Formula:KLS:01.06:01

formula in Some integrals

Formula:KLS:01.06:03 >>

${\displaystyle{\displaystyle{\displaystyle{}{}\frac{\Gamma\left(a\right)\Gamma\left(b\right)}{\Gamma\left(c\right)}\,\HyperpFq{2}{1}@@{a,b}{c}{z}=\frac{1}{2\pi\mathrm{i}}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(a+s\right)\Gamma\left(b+s\right)\Gamma\left(-s\right)}{\Gamma\left(c+s\right)}(-z)^{s}\,ds}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv

Bibliography

Equation in Section 1.6 of KLS.

URL links

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<< Formula:KLS:01.06:01

formula in Some integrals

Formula:KLS:01.06:03 >>