Formula:KLS:09.08:90

<< Formula:KLS:09.08:89

formula in Jacobi: Special cases

Formula:KLS:09.08:91 >>

${\displaystyle{\displaystyle{\displaystyle\LegendrePoly{n}@{x}=\binomial{2n}{n}\frac{1}{2^{n}}{\widehat{P}}_{n}\left(x\right){x}}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}}}}$ : monic Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:monicLegendrePoly

Bibliography

Equation in Section 9.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.08:89

formula in Jacobi: Special cases

Formula:KLS:09.08:91 >>