Formula:KLS:01.05:05

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formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:06 >>

${\displaystyle{\displaystyle{\displaystyle{}{}{}{}\HyperpFq{3}{2}@@{-n,a,b}{c,1+a+b-c-n}{1}=\frac{{\left(c-a\right)_{n}}{\left(c-b\right)_{n}}}{{\left(c\right)_{n}}{\left(c-a-b\right)_{n}}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=0,1,2,\ldots}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 1.5 of KLS.

URL links

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<< Formula:KLS:01.05:04

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:06 >>