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http://functions.wolfram.com/07.14.06.0026.01
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GegenbauerC[\[Nu], \[Lambda], z] ==
((2^\[Nu] Gamma[\[Nu] + \[Lambda]])/(Gamma[\[Nu] + 1] Gamma[\[Lambda]]))
(z - 1)^\[Nu] Hypergeometric2F1[-\[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]) Hypergeometric2F1[\[Nu] + 2 \[Lambda],
1/2 + \[Nu] + \[Lambda], 1 + 2 \[Nu] + 2 \[Lambda], 2/(1 - z)] /;
!IntervalMemberQ[Interval[{-1, 1}], z] &&
!Element[2 \[Lambda] + 2 \[Nu], Integers]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <mi> C </mi> <mi> ν </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <mrow> <msup> <mn> 2 </mn> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> λ </mi> <mo> + </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> λ </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> λ </mi> </mrow> <mo> - </mo> <mi> ν </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; 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Date Added to functions.wolfram.com (modification date)
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