Formula:KLS:01.05:06

<< Formula:KLS:01.05:05

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:07 >>

${\displaystyle{\displaystyle{\displaystyle{}\HyperpFq{5}{4}@@{1+a/2,a,b,c,d}{a/2,1+a-b,1+a-c,1+a-d}{1}{}=\frac{\Gamma\left(1+a-b\right)\Gamma\left(1+a-c\right)\Gamma\left(1+a-d\right)\Gamma\left(1+a-b-c-d\right)}{\Gamma\left(1+a\right)\Gamma\left(1+a-b-c\right)\Gamma\left(1+a-b-d\right)\Gamma\left(1+a-c-d\right)}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section 1.5 of KLS.

URL links

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<< Formula:KLS:01.05:05

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:07 >>