Formula:KLS:09.01:10

<< Formula:KLS:09.01:09

formula in Wilson

Formula:KLS:09.01:11 >>

${\displaystyle{\displaystyle{\displaystyle W_{n}\!\left(x^{2};a,b,c,d\right)=(-1)^{n}{\left(n+a+b+c+d-1\right)_{n}}{\widehat{W}}_{n}\!\left(x^{2}\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle{\widehat{W}}_{n}}}}$ : monic Wilson polynomial : http://drmf.wmflabs.org/wiki/Definition:monicWilson

Bibliography

Equation in Section 9.1 of KLS.

URL links

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<< Formula:KLS:09.01:09

formula in Wilson

Formula:KLS:09.01:11 >>