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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/07.14.06.0059.01









  


  








Input Form





GegenbauerC[\[Nu], \[Lambda], z] == (-((Sqrt[Pi] (2 - 2 z)^(1/2 - \[Lambda]) Sec[Pi (\[Lambda] + \[Nu])] Sin[Pi \[Nu]])/Gamma[\[Lambda]])) Sum[((Pochhammer[1/2 - \[Lambda] - \[Nu], k] Pochhammer[1/2 + \[Lambda] + \[Nu], k])/(Gamma[3/2 - \[Lambda] + k] k!)) ((1 - z)/2)^k, {k, 0, Infinity}] /; 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