Formula:KLS:09.01:09

<< Formula:KLS:09.01:06

formula in Wilson

Formula:KLS:09.01:10 >>

${\displaystyle{\displaystyle{\displaystyle x\monicWilson{n}@@{x}{a}{b}{c}{d}=\monicWilson{n+1}@@{x}{a}{b}{c}{d}+(A_{n}+C_{n}-a^{2})\monicWilson{n}@@{x}{a}{b}{c}{d}+A_{n-1}C_{n}\monicWilson{n-1}@@{x}{a}{b}{c}{d}}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle C_{n}=\frac{n(n+b+c-1)(n+b+d-1)(n+c+d-1)}{(2n+a+b+c+d-2)(2n+a+b+c+d-1)}}}}$ &
${\displaystyle{\displaystyle{\displaystyle A_{n}=\frac{(n+a+b+c+d-1)(n+a+b)(n+a+c)(n+a+d)}{(2n+a+b+c+d-1)(2n+a+b+c+d)}}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle{\widehat{W}}_{n}}}}$ : 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:09.01:06

formula in Wilson

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