Formula:KLS:01.05:03

<< Formula:KLS:01.05:02

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:04 >>

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

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{c-a-b}>0}}}$

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
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation in Section 1.5 of KLS.

URL links

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<< Formula:KLS:01.05:02

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:04 >>