Formula:KLS:09.08:18

<< Formula:KLS:09.08:17

formula in Jacobi: Special cases

Formula:KLS:09.08:19 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle C^{\mu}_{n}}}}$ : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:17

formula in Jacobi: Special cases

Formula:KLS:09.08:19 >>