Formula:KLS:01.05:01

<< Hypergeometric functions

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:02 >>

${\displaystyle{\displaystyle{\displaystyle{}{}\HyperpFq{1}{0}@@{a}{-}{z}=\sum_{n=0}^{\infty}\frac{{\left(a\right)_{n}}}{n!}z^{n}=(1-z)^{-a}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle|z|<1}}}$

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 1.5 of KLS.

URL links

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<< Hypergeometric functions

formula in The binomial theorem and other summation formulas

Formula:KLS:01.05:02 >>