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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/(1-z)





http://functions.wolfram.com/07.14.06.0029.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] \[Proportional] (((-1)^(\[Nu] + \[Lambda] - 1) 2^(1 - \[Nu] - 2 \[Lambda]) Sin[\[Nu] Pi] Gamma[\[Nu] + 2 \[Lambda]])/(Pi Gamma[\[Lambda]] Gamma[1 + \[Nu] + \[Lambda]])) z^(-\[Nu] - 2 \[Lambda]) (Log[(z - 1)/2] - EulerGamma - PolyGamma[1/2 - \[Lambda] - \[Nu]] - PolyGamma[2 \[Lambda] + \[Nu]] + PolyGamma[1 + 2 \[Lambda] + 2 \[Nu]]) (1 + O[1/z]) + ((2^\[Nu] Gamma[\[Lambda] + \[Nu]])/ (Gamma[\[Lambda]] Gamma[1 + \[Nu]])) z^\[Nu] (1 + O[1/z]) /; (Abs[z] -> Infinity) && Element[\[Lambda] + \[Nu], Integers] && \[Lambda] + \[Nu] > 0 && !Element[\[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)





2001-10-29





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