Formula:KLS:09.06:24

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formula in Dual Hahn

Formula:KLS:09.06:25 >>

${\displaystyle{\displaystyle{\displaystyle\left[(1-t)^{-\epsilon}\,\HyperpFq{3}{2}@@{\epsilon,-x,x+\gamma+\delta+1}{\gamma+1,-N}{\frac{t}{t-1}}\right]_{N}{}=\sum_{n=0}^{N}\frac{{\left(\epsilon\right)_{n}}}{n!}R_{n}\!\left(\lambda(x);\gamma,\delta,N\right)t^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\epsilon}}}$ arbitrary

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle\lambda(x)=x(x+\gamma+\delta+1)}}}$

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
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r5

Bibliography

Equation in Section 9.6 of KLS.

URL links

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<< Formula:KLS:09.06:23

formula in Dual Hahn

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