# Formula:KLS:01.06:05

${\displaystyle{\displaystyle{\displaystyle{}\frac{1}{2\cpi\iunit}\int_{-\iunit% \infty}^{\iunit\infty}\frac{\Gamma\left(1+a/2+s\right)\Gamma\left(a+s\right)% \Gamma\left(b+s\right)\Gamma\left(c+s\right)\Gamma\left(d+s\right)\Gamma\left(% b-a-s\right)\Gamma\left(-s\right)}{\Gamma\left(a/2+s\right)\Gamma\left(1+a-c+s% \right)\Gamma\left(1+a-d+s\right)}\,ds{}=\frac{\Gamma\left(b\right)\Gamma\left% (c\right)\Gamma\left(d\right)\Gamma\left(b+c-a\right)\Gamma\left(b+d-a\right)}% {2\,\Gamma\left(1+a-c-d\right)\Gamma\left(b+c+d-a\right)}}}}$

## Proof

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## Symbols List

: ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
: integral : http://dlmf.nist.gov/1.4#iv
: Euler's gamma function : http://dlmf.nist.gov/5.2#E1