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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/z





http://functions.wolfram.com/07.14.06.0072.01









  


  










Input Form





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










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





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