Formula:KLS:09.06:01

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formula in Dual Hahn

Formula:KLS:09.06:03 >>

${\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\lambda(x);\gamma,\delta,N\right)=\HyperpFq{3}{2}@@{-n,-x,x+\gamma+\delta+1}{\gamma+1,-N}{1}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=0,1,2,\ldots,N}}}$

Substitution(s)

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r5
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 9.6 of KLS.

URL links

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<< Hahn

formula in Dual Hahn

Formula:KLS:09.06:03 >>