Formula:KLS:01.03:01

<< The gamma and beta function

formula in The shifted factorial and binomial coefficients

Formula:KLS:01.03:02 >>

${\displaystyle{\displaystyle{\displaystyle{}{\left(a\right)_{0}}:=1\quad\textrm{and}\quad{\left(a\right)_{k}}:=\prod_{n=1}^{k}(a+n-1),\quad k=1,2,3,\ldots}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle\Pi}}}$ : product : http://drmf.wmflabs.org/wiki/Definition:prod

Bibliography

Equation in Section 1.3 of KLS.

URL links

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<< The gamma and beta function

formula in The shifted factorial and binomial coefficients

Formula:KLS:01.03:02 >>