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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/07.14.06.0024.02









  


  










Input Form





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