Formula:KLS:09.08:86

<< Formula:KLS:09.08:85

formula in Jacobi: Special cases

Formula:KLS:09.08:87 >>

${\displaystyle{\displaystyle{\displaystyle\LegendrePoly{n}@{x}=P^{(0,0)}_{n}\left(x\right)=\HyperpFq{2}{1}@@{-n,n+1}{1}{\frac{1-x}{2}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 9.8 of KLS.

URL links

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<< Formula:KLS:09.08:85

formula in Jacobi: Special cases

Formula:KLS:09.08:87 >>