Formula:KLS:09.15:01

<< Charlier

formula in Hermite

Formula:KLS:09.15:02 >>

${\displaystyle{\displaystyle{\displaystyle H_{n}\left(x\right)=(2x)^{n}\,\HyperpFq{2}{0}@@{-n/2,-(n-1)/2}{-}{-\frac{1}{x^{2}}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 9.15 of KLS.

URL links

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<< Charlier

formula in Hermite

Formula:KLS:09.15:02 >>