Formula:KLS:09.10:15

<< Formula:KLS:09.10:14

formula in Meixner

Formula:KLS:09.10:16 >>

${\displaystyle{\displaystyle{\displaystyle(1-t)^{-\gamma}\,\HyperpFq{2}{1}@@{\gamma,-x}{\beta}{\frac{(1-c)t}{c(1-t)}}=\sum_{n=0}^{\infty}\frac{{\left(\gamma\right)_{n}}}{n!}M_{n}\!\left(x;\beta,c\right)t^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\gamma}}}$ arbitrary

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : 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

Bibliography

Equation in Section 9.10 of KLS.

URL links

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