Formula:KLS:09.12:34

<< Formula:KLS:09.12:33

formula in Laguerre

Formula:KLS:09.12:35 >>

${\displaystyle{\displaystyle{\displaystyle H^{\mu}_{2m}\left(x\right)=\frac{(-1)^{m}(2m)!}{{\left(\mu+\frac{1}{2}\right)_{m}}}L^{\mu-\frac{1}{2}}_{m}\left(x^{2}\right),\qquad H^{\mu}_{2m+1}\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle H_{n}^{\mu}}}}$ : generalized Hermite polynomial : http://drmf.wmflabs.org/wiki/Definition:GenHermite
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : 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 in Laguerre

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