Formula:KLS:09.05:19

<< Formula:KLS:09.05:18

formula in Hahn

Formula:KLS:09.05:20 >>

${\displaystyle{\displaystyle{\displaystyle\HyperpFq{1}{1}@@{-x}{\alpha+1}{-t}\,\HyperpFq{1}{1}@@{x-N}{\beta+1}{t}=\sum_{n=0}^{N}\frac{{\left(-N\right)_{n}}}{{\left(\beta+1\right)_{n}}n!}Q_{n}\!\left(x;\alpha,\beta,N\right)t^{n}}}}$

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
${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : Hahn polynomial : http://dlmf.nist.gov/18.19#T1.t1.r3

Bibliography

Equation in Section 9.5 of KLS.

URL links

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<< Formula:KLS:09.05:18

formula in Hahn

Formula:KLS:09.05:20 >>