Formula:KLS:09.15:25

<< Formula:KLS:09.15:24

formula in Hermite

Formula:KLS:09.15:26 >>

${\displaystyle{\displaystyle{\displaystyle\frac{H_{n}\left(x\right)}{n!}=\sum_{k=0}^{\lfloor n/2\rfloor}\frac{(-1)^{k}(2x)^{n-2k}}{k!\,(n-2k)!}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation in Section 9.15 of KLS.

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<< Formula:KLS:09.15:24

formula in Hermite

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