Formula:KLS:09.12:15

<< Formula:KLS:09.12:14

formula in Laguerre

Formula:KLS:09.12:16 >>

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

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
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : 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:KLS:09.12:14

formula in Laguerre

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