Formula:KLS:09.10:20

<< Formula:KLS:09.10:19

formula in Meixner

Formula:KLS:09.10:21 >>

${\displaystyle{\displaystyle{\displaystyle\frac{{\left(\beta\right)_{n}}}{n!}M_{n}\!\left(x;\beta,c\right)=P^{(\beta-1,-n-\beta-x)}_{n}\left((2-c\right)c^{-1})}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : Meixner polynomial : http://dlmf.nist.gov/18.19#T1.t1.r9
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 9.10 of KLS.

URL links

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Formula:KLS:09.10:21 >>