Formula:KLS:09.12:01

<< Krawtchouk

formula in Laguerre

Formula:KLS:09.12:02 >>

${\displaystyle{\displaystyle{\displaystyle L^{\alpha}_{n}\left(x\right)=\frac{{\left(\alpha+1\right)_{n}}}{n!}\,\HyperpFq{1}{1}@@{-n}{\alpha+1}{x}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 9.12 of KLS.

URL links

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<< Krawtchouk

formula in Laguerre

Formula:KLS:09.12:02 >>