Formula:KLS:01.04:01

<< The shifted factorial and binomial coefficients

formula in Hypergeometric functions

Formula:KLS:01.04:02 >>

${\displaystyle{\displaystyle{\displaystyle{}\HyperpFq{r}{s}@@{a_{1},\ldots,a_{r}}{b_{1},\ldots,b_{s}}{z}:=\sum\limits_{k=0}^{\infty}\frac{{\left(a_{1},\ldots,a_{r}\right)_{k}}}{{\left(b_{1},\ldots,b_{s}\right)_{k}}}\frac{z^{k}}{k!}}}}$

Proof

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Symbols List

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

Bibliography

Equation in Section 1.4 of KLS.

URL links

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<< The shifted factorial and binomial coefficients

formula in Hypergeometric functions

Formula:KLS:01.04:02 >>