Formula:KLS:09.08:90

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \LegendrePoly{n}@{x}=\binomial{2n}{n}\frac{1}{2^n}\monicLegendrePoly{n}@@{x}{x} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle P_{n}}}  : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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

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