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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 generic point z==z0 > For the function itself





http://functions.wolfram.com/07.14.06.0041.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] \[Proportional] (-((2^(1 - 2 \[Lambda]) Cos[Pi (\[Lambda] + \[Nu])] Sin[Pi \[Nu]])/ (Pi^(3/2) Gamma[\[Lambda]]))) (I Pi^(3/2) 4^\[Lambda] E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Csc[Pi \[Nu]] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[1 + Subscript[z, 0]])/(2 Pi)] Gamma[\[Lambda]] GegenbauerC[\[Nu], \[Lambda], Subscript[z, 0]] + (1/(1 + Subscript[z, 0]))^((1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (1 + Subscript[z, 0])^ ((1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) MeijerG[{{1 + \[Nu], 1 - 2 \[Lambda] - \[Nu]}, {}}, {{0, 1/2 - \[Lambda]}, {}}, (1/2) (1 + Subscript[z, 0])] + O[z - Subscript[z, 0]])










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





© 1998- Wolfram Research, Inc.