Gegenbauer function: Representations through more general functions (formula 07.14.26.0004)

GegenbauerC

$Mathematica Notation$

Hypergeometric Functions

GegenbauerC[nu,lambda,z]

Representations through more general functions

Through hypergeometric functions

Involving ₂F₁

http://functions.wolfram.com/07.14.26.0004.01

Input Form

GegenbauerC[\[Nu], \[Lambda], z] == ((2^\[Nu] Gamma[\[Nu] + \[Lambda]])/(Gamma[\[Nu] + 1] Gamma[\[Lambda]])) (z - 1)^\[Nu] HypergeometricPFQ[{-\[Nu], 1/2 - \[Nu] - \[Lambda]}, {1 - 2 \[Nu] - 2 \[Lambda]}, 2/(1 - z)] - ((2^(-\[Nu] - 2 \[Lambda]) Sin[\[Nu] Pi])/(Pi Gamma[\[Lambda]])) Gamma[-\[Nu] - \[Lambda]] Gamma[\[Nu] + 2 \[Lambda]] (z - 1)^(-\[Nu] - 2 \[Lambda]) HypergeometricPFQ[ {\[Nu] + 2 \[Lambda], 1/2 + \[Nu] + \[Lambda]}, {1 + 2 \[Nu] + 2 \[Lambda]}, 2/(1 - z)] /; !Element[2 \[Lambda] + 2 \[Nu], 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[n,lambda,z]