Formula:KLS:09.12:14

<< Formula:KLS:09.12:13

formula in Laguerre

Formula:KLS:09.12:15 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{\phi\rightarrow 0}P^{(\frac{1}{2}\alpha+\frac{1}{2})}_{n}\!\left(-\textstyle\frac{1}{2}\phi^{-1}x;\phi\right)=L^{\alpha}_{n}\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$ : Meixner-Pollaczek polynomial : http://dlmf.nist.gov/18.19#P3.p1
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : 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:09.12:13

formula in Laguerre

Formula:KLS:09.12:15 >>