Formula:KLS:09.01:17

<< Formula:KLS:09.01:16

formula in Wilson

Formula:KLS:09.01:18 >>

${\displaystyle{\displaystyle{\displaystyle(a-\textstyle\frac{1}{2}-\iunit x)(b-\textstyle\frac{1}{2}-\iunit x)(c-\textstyle\frac{1}{2}-\iunit x)(d-\textstyle\frac{1}{2}-\iunit x)\Wilson{n}@{(x+\textstyle\frac{1}{2}\iunit)^{2}}{a}{b}{c}{d}{}-(a-\textstyle\frac{1}{2}+\iunit x)(b-\textstyle\frac{1}{2}+\iunit x)(c-\textstyle\frac{1}{2}+\iunit x)(d-\textstyle\frac{1}{2}+\iunit x)\Wilson{n}@{(x-\textstyle\frac{1}{2}\iunit)^{2}}{a}{b}{c}{d}{}=-2\iunit x\Wilson{n+1}@{x^{2}}{a-\textstyle\frac{1}{2}}{b-\textstyle\frac{1}{2}}{c-\textstyle\frac{1}{2}}{d-\textstyle\frac{1}{2}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle W_{n}}}}$ : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2

Bibliography

Equation in Section 9.1 of KLS.

URL links

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<< Formula:KLS:09.01:16

formula in Wilson

Formula:KLS:09.01:18 >>