Formula:KLS:09.12:13

<< Formula:KLS:09.12:12

formula in Laguerre

Formula:KLS:09.12:14 >>

${\displaystyle{\displaystyle{\displaystyle(1-t)^{-\gamma}\,\HyperpFq{1}{1}@@{\gamma}{\alpha+1}{\frac{xt}{t-1}}=\sum_{n=0}^{\infty}\frac{{\left(\gamma\right)_{n}}}{{\left(\alpha+1\right)_{n}}}L^{\alpha}_{n}\left(x\right)t^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\gamma}}}$ arbitrary

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27

Bibliography

Equation in Section 9.12 of KLS.

URL links

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<< Formula:KLS:09.12:12

formula in Laguerre

Formula:KLS:09.12:14 >>