Formula:KLS:09.08:97

<< Formula:KLS:09.08:96

formula in Jacobi: Special cases

Formula:KLS:09.09:01 >>

${\displaystyle{\displaystyle{\displaystyle(1-xt)^{-\gamma}\,\HyperpFq{2}{1}@@{\frac{1}{2}\gamma,\frac{1}{2}\gamma+\frac{1}{2}}{1}{\frac{(x^{2}-1)t^{2}}{(1-xt)^{2}}}{}=\sum_{n=0}^{\infty}\frac{{\left(\gamma\right)_{n}}}{n!}\LegendrePoly{n}@{x}t^{n}}}}$

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
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:96

formula in Jacobi: Special cases

Formula:KLS:09.09:01 >>