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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==0 > For the function itself > General case





http://functions.wolfram.com/07.14.06.0050.01









  


  








Input Form





GegenbauerC[\[Nu], \[Lambda], z] == ((Cos[(Pi \[Nu])/2] Gamma[\[Nu]/2 + \[Lambda]])/(Gamma[\[Nu]/2 + 1] Gamma[\[Lambda]])) Hypergeometric2F1[-(\[Nu]/2), \[Lambda] + \[Nu]/2, 1/2, z^2] + ((2^\[Nu] Sqrt[Pi] Gamma[\[Lambda] + (1 + \[Nu])/2] z)/ (Gamma[\[Lambda]] Gamma[1 - \[Nu]/2] Gamma[\[Nu]])) Hypergeometric2F1[(1 - \[Nu])/2, \[Lambda] + (\[Nu] + 1)/2, 3/2, z^2]








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