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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==1 > For the function itself > Special cases





http://functions.wolfram.com/07.14.06.0058.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] \[Proportional] (-((Sqrt[Pi] (2 - 2 z)^(1/2 - \[Lambda]) Sec[Pi (\[Lambda] + \[Nu])] Sin[Pi \[Nu]])/(Gamma[\[Lambda]] Gamma[3/2 - \[Lambda]]))) (1 + (((-1 + 2 \[Lambda] + 2 \[Nu]) (1 + 2 \[Lambda] + 2 \[Nu]))/ (4 (3 - 2 \[Lambda]))) (z - 1) + (((-3 + 2 \[Lambda] + 2 \[Nu]) (-1 + 2 \[Lambda] + 2 \[Nu]) (1 + 2 \[Lambda] + 2 \[Nu]) (3 + 2 \[Lambda] + 2 \[Nu]))/ (32 (3 - 2 \[Lambda]) (5 - 2 \[Lambda]))) (z - 1)^2 + O[(z - 1)^3]) /; Element[-\[Lambda] - 1/2, Integers] && -\[Lambda] - 1/2 >= 0










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)





2007-05-02