Formula:KLS:01.06:01

<< The binomial theorem and other summation formulas

formula in Some integrals

Formula:KLS:01.06:02 >>

${\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{2}{1}@@{a,b}{c}{z}=\frac{\Gamma\left(c\right)}{\Gamma\left(b\right)\Gamma\left(c-b\right)}\int_{0}^{1}t^{b-1}(1-t)^{c-b-1}(1-zt)^{-a}\,dt}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv

Bibliography

Equation in Section 1.6 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< The binomial theorem and other summation formulas

formula in Some integrals

Formula:KLS:01.06:02 >>