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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/07.14.06.0040.01









  


  








Input Form





GegenbauerC[\[Nu], \[Lambda], z] == ((2^(1 - 2 \[Lambda]) Sin[Pi \[Nu]])/(Sqrt[Pi] Gamma[\[Lambda]])) Sum[(1/(2^k k!)) (Gamma[k - \[Nu]] Gamma[k + 2 \[Lambda] + \[Nu]] Cos[Pi (\[Lambda] + \[Nu])] (2 I E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Floor[(Pi + Arg[1 + Subscript[z, 0]])/(2 Pi)] Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] - Sec[Pi \[Lambda]] (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)])) Hypergeometric2F1Regularized[k - \[Nu], k + 2 \[Lambda] + \[Nu], 1/2 + k + \[Lambda], (1 + Subscript[z, 0])/2] + 2^(-(1/2) + k + \[Lambda]) Pi Sec[Pi \[Lambda]] (1/(1 + Subscript[z, 0]))^((1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (1 + Subscript[z, 0])^ (1/2 - k - \[Lambda] + (1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) Hypergeometric2F1Regularized[1/2 + \[Lambda] + \[Nu], 1/2 - \[Lambda] - \[Nu], 3/2 - k - \[Lambda], (1 + Subscript[z, 0])/ 2]) (z - Subscript[z, 0])^k, {k, 0, Infinity}] /; !Element[1/2 - \[Lambda], 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)





2007-05-02