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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/07.14.06.0032.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] \[Proportional] (((-1)^(\[Nu] + \[Lambda]) 2^(\[Nu] + 1))/(Gamma[\[Nu] + 1] Gamma[1 - \[Nu] - \[Lambda]] Gamma[\[Lambda]])) z^\[Nu] (Log[(z - 1)/2] - EulerGamma + PolyGamma[1 - 2 \[Lambda] - 2 \[Nu]] - PolyGamma[-\[Nu]] - PolyGamma[1/2 + \[Lambda] + \[Nu]]) (1 + O[1/z]) - ((2^(-2 \[Lambda] - \[Nu]) Gamma[-\[Lambda] - \[Nu]] Gamma[2 \[Lambda] + \[Nu]] Sin[Pi \[Nu]])/(Pi Gamma[\[Lambda]])) z^(-\[Nu] - 2 \[Lambda]) (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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2001-10-29





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