Gegenbauer function: Representations through more general functions (formula 07.14.26.0010)

GegenbauerC

$Mathematica Notation$

Hypergeometric Functions

GegenbauerC[nu,lambda,z]

Representations through more general functions

Through Meijer G

Classical cases involving algebraic functions

http://functions.wolfram.com/07.14.26.0010.01

Input Form

(1 + z)^(\[Lambda] - 1/2) GegenbauerC[\[Nu], \[Lambda], 2/z + 1] == ((Cos[(\[Lambda] + \[Nu]) Pi] Pochhammer[2 \[Lambda], \[Nu]])/ (Cos[\[Lambda] Pi] Gamma[1/2 - \[Lambda]] Gamma[\[Nu] + 1])) MeijerG[{{\[Lambda] + 1/2}, {2 \[Lambda]}}, {{-\[Nu], 2 \[Lambda] + \[Nu]}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]

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[n,lambda,z]