Formula:KLS:09.15:23

<< Formula:KLS:09.15:22

formula in Hermite

Formula:KLS:09.15:24 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{\alpha\rightarrow\infty}\left(\frac{2}{\alpha}\right)^{\frac{1}{2}n}L^{\alpha}_{n}\left((2\alpha\right)^{\frac{1}{2}}x+\alpha)=\frac{(-1)^{n}}{n!}H_{n}\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : 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:09.15:22

formula in Hermite

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