Gegenbauer polynomials: Representations through more general functions (formula 05.09.26.0003)

GegenbauerC

$Mathematica Notation$

Polynomials

GegenbauerC[n,lambda,z]

Representations through more general functions

Through hypergeometric functions

Involving ₂F₁

http://functions.wolfram.com/05.09.26.0003.01

Input Form

GegenbauerC[n, \[Lambda], z] == ((Cos[Pi (n + \[Lambda])] Sec[Pi \[Lambda]] Gamma[n + 2 \[Lambda]])/ (Gamma[n + 1] Gamma[2 \[Lambda]])) HypergeometricPFQ[ {-n, n + 2 \[Lambda]}, {1/2 + \[Lambda]}, (1 + z)/2] /; !Element[\[Lambda] + 1/2, Integers]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

GegenbauerC[nu,z]
GegenbauerC[nu,lambda,z]