Formula:KLS:09.15:19

<< Formula:KLS:09.15:18

formula in Hermite

Formula:KLS:09.15:20 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{\lambda\rightarrow\infty}\lambda^{-\frac{1}{2}n}P^{(\lambda)}_{n}\!\left((\sin\phi)^{-1}(x\sqrt{\lambda}-\lambda\cos\phi);\phi\right)=\frac{H_{n}\left(x\right)}{n!}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$ : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1
${\displaystyle{\displaystyle{\displaystyle\mathrm{sin}}}}$ : sine function : http://dlmf.nist.gov/4.14#E1
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : 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:09.15:18

formula in Hermite

Formula:KLS:09.15:20 >>