Formula:KLS:09.03:25

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formula in Continuous dual Hahn

Formula:KLS:09.03:26 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{d\rightarrow\infty}\frac{W_{n}\!\left(x^{2};a,b,c,d\right)}{{\left(a+d\right)_{n}}}=S_{n}\!\left(x^{2};a,b,c\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle W_{n}}}}$ : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : continuous dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r3

Bibliography

Equation in Section 9.3 of KLS.

URL links

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formula in Continuous dual Hahn

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