Gegenbauer function: Representations through more general functions (formula 07.14.26.0029)

GegenbauerC

$Mathematica Notation$

Hypergeometric Functions

GegenbauerC[nu,lambda,z]

Representations through more general functions

Through Meijer G

Classical cases involving unit step theta

http://functions.wolfram.com/07.14.26.0029.01

Input Form

UnitStep[1 - Abs[z]] (1 - z)^(-1 + 2 \[Lambda]) GegenbauerC[\[Nu], \[Lambda], (1 + z)/(2 Sqrt[z])] == (1/Gamma[1 + \[Nu]]) Gamma[2 \[Lambda] + \[Nu]] MeijerG[{{}, {\[Lambda] - \[Nu]/2, 2 \[Lambda] + \[Nu]/2}}, {{\[Lambda] + \[Nu]/2, -(\[Nu]/2)}, {}}, 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]