Formula:KLS:09.15:20

<< Formula:KLS:09.15:19

formula in Hermite

Formula:KLS:09.15:21 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : 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:09.15:19

formula in Hermite

Formula:KLS:09.15:21 >>