Formula:KLS:09.15:10

<< Formula:KLS:09.15:09

formula in Hermite

Formula:KLS:09.15:11 >>

${\displaystyle{\displaystyle{\displaystyle{\mathrm{e}^{-x^{2}}}H_{n}\left(x\right)=(-1)^{n}\left(\frac{d}{dx}\right)^{n}\left[{\mathrm{e}^{-x^{2}}}\right]}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : 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:KLS:09.15:09

formula in Hermite

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