Formula:KLS:09.10:18

<< Formula:KLS:09.10:17

formula in Meixner

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${\displaystyle{\displaystyle{\displaystyle\lim_{c\rightarrow 1}M_{n}\!\left((1-c)^{-1}x;\alpha+1,c\right)=\frac{L^{\alpha}_{n}\left(x\right)}{L^{\alpha}_{n}\left(0\right)}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : Meixner polynomial : http://dlmf.nist.gov/18.19#T1.t1.r9
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27

Bibliography

Equation in Section 9.10 of KLS.

URL links

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<< Formula:KLS:09.10:17

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