Formula:KLS:09.01:22

<< Formula:KLS:09.01:21

formula in Wilson

Formula:KLS:09.01:23 >>

${\displaystyle{\displaystyle{\displaystyle\HyperpFq{2}{1}@@{a+\mathrm{i}x,c+\mathrm{i}x}{a+c}{t}\,\HyperpFq{2}{1}@@{b-\mathrm{i}x,d-\mathrm{i}x}{b+d}{t}=\sum_{n=0}^{\infty}\frac{W_{n}\!\left(x^{2};a,b,c,d\right)t^{n}}{{\left(a+c\right)_{n}}{\left(b+d\right)_{n}}n!}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle W_{n}}}}$ : 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

Bibliography

Equation in Section 9.1 of KLS.

URL links

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<< Formula:KLS:09.01:21

formula in Wilson

Formula:KLS:09.01:23 >>