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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/07.14.06.0038.01









  


  










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])] + (1/2) (2 Pi I E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[1 + Subscript[z, 0]])/(2 Pi)] Gamma[1 - \[Nu]] Gamma[1 + 2 \[Lambda] + \[Nu]] Hypergeometric2F1Regularized[1 - \[Nu], 1 + 2 \[Lambda] + \[Nu], 3/2 + \[Lambda], (1/2) (1 + 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[{{\[Nu], -2 \[Lambda] - \[Nu]}, {}}, {{0, -(1/2) - \[Lambda]}, {}}, (1/2) (1 + Subscript[z, 0])]) (z - Subscript[z, 0]) + (1/8) (2 Pi I E^(I Pi (1/2 - \[Lambda]) Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)]) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] Floor[(Pi + Arg[1 + Subscript[z, 0]])/(2 Pi)] Gamma[2 - \[Nu]] Gamma[2 + 2 \[Lambda] + \[Nu]] Hypergeometric2F1Regularized[2 - \[Nu], 2 + 2 \[Lambda] + \[Nu], 5/2 + \[Lambda], (1/2) (1 + 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, -(3/2) - \[Lambda]}, {}}, (1/2) (1 + Subscript[z, 0])]) (z - Subscript[z, 0])^2 + O[(z - Subscript[z, 0])^3])










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