Formula:KLS:09.12:22

<< Formula:KLS:09.12:21

formula in Laguerre

Formula:KLS:09.12:23 >>

${\displaystyle{\displaystyle{\displaystyle H_{2n+1}\left(x\right)=(-1)^{n}n!\,2^{2n+1}xL^{\frac{1}{2}}_{n}\left(x^{2}\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27

Bibliography

Equation in Section 9.12 of KLS.

URL links

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<< Formula:KLS:09.12:21

formula in Laguerre

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