Formula:KLS:09.03:05

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formula in Continuous dual Hahn

Formula:KLS:09.03:08 >>

${\displaystyle{\displaystyle{\displaystyle{\tilde{S}}_{n}\!\left(x^{2}\right):={\tilde{S}}_{n}\!\left(x^{2};a,b,c\right)=\frac{S_{n}\!\left(x^{2};a,b,c\right)}{{\left(a+b\right)_{n}}{\left(a+c\right)_{n}}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{\tilde{S}}_{n}}}}$ : normalized continuous dual Hahn polynomial ${\displaystyle{\displaystyle{\displaystyle{\tilde{S}}}}}$ : http://drmf.wmflabs.org/wiki/Definition:normctsdualHahnStilde
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : continuous dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.3 of KLS.

URL links

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formula in Continuous dual Hahn

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