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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/07.14.06.0069.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] \[Proportional] ((2^\[Nu] Gamma[\[Lambda] + \[Nu]])/(Gamma[\[Lambda]] Gamma[1 + \[Nu]])) z^\[Nu] (1 - ((1 - \[Nu]) \[Nu])/(4 (1 - \[Lambda] - \[Nu]) z^2) + ((-3 + \[Nu]) (-2 + \[Nu]) (-1 + \[Nu]) \[Nu])/ (32 (-2 + \[Lambda] + \[Nu]) (-1 + \[Lambda] + \[Nu]) z^4) + \[Ellipsis]) - ((2^(-2 \[Lambda] - \[Nu]) Sin[Pi \[Nu]] Gamma[-\[Lambda] - \[Nu]] Gamma[2 \[Lambda] + \[Nu]])/ (Pi Gamma[\[Lambda]])) z^(-\[Nu] - 2 \[Lambda]) (1 + ((2 \[Lambda] + \[Nu]) (1 + 2 \[Lambda] + \[Nu]))/ (4 (1 + \[Lambda] + \[Nu]) z^2) + ((2 \[Lambda] + \[Nu]) (1 + 2 \[Lambda] + \[Nu]) (2 + 2 \[Lambda] + \[Nu]) (3 + 2 \[Lambda] + \[Nu]))/ (32 (1 + \[Lambda] + \[Nu]) (2 + \[Lambda] + \[Nu]) z^4) + \[Ellipsis]) /; (Abs[z] -> Infinity) && !Element[\[Lambda] + \[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)





2007-05-02





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