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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Expansions in 1/(1-z)





http://functions.wolfram.com/07.14.06.0035.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] == (-((2^(-\[Nu] - 2 \[Lambda]) Gamma[-\[Nu] - \[Lambda]] Gamma[\[Nu] + 2 \[Lambda]] Sin[\[Nu] Pi])/(Pi Gamma[\[Lambda]]))) (z - 1)^(-\[Nu] - 2 \[Lambda]) Sum[((Pochhammer[1/2 + \[Nu] + \[Lambda], k] Pochhammer[ \[Nu] + 2 \[Lambda], k])/(k! Pochhammer[1 + 2 \[Nu] + 2 \[Lambda], k])) (2/(1 - z))^k, {k, 0, -(1/2) - \[Nu] - \[Lambda]}] + (((-1)^(1/2 - \[Nu] - \[Lambda]) 2^(\[Nu] + 1) Pi)/ (Gamma[\[Nu] + 1] Gamma[1 - \[Nu] - \[Lambda]] Gamma[\[Lambda]])) (z - 1)^\[Nu] Hypergeometric2F1[-\[Nu], 1/2 - \[Nu] - \[Lambda], 1 - 2 \[Nu] - 2 \[Lambda], 2/(1 - z)] /; Element[-\[Lambda] - \[Nu] - 1/2, Integers] && -\[Lambda] - \[Nu] - 1/2 >= 0 && !Element[\[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





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