Formula:KLS:09.15:11

<< Formula:KLS:09.15:10

formula in Hermite

Formula:KLS:09.15:12 >>

${\displaystyle{\displaystyle{\displaystyle\exp\left(2xt-t^{2}\right)=\sum_{n=0}^{\infty}\frac{H_{n}\left(x\right)}{n!}t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{exp}}}}$ : exponential function : http://dlmf.nist.gov/4.2#E19
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 9.15 of KLS.

URL links

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formula in Hermite

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