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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/07.13.06.0035.01









  


  










Input Form





GegenbauerC[\[Nu], z] \[Proportional] (2/\[Nu]) (Sin[Pi \[Nu]] Sqrt[1 - Subscript[z, 0]^2] ChebyshevU[\[Nu] - 1, -Subscript[z, 0]] (1/(1 + Subscript[z, 0]))^ ((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (1 + Subscript[z, 0])^((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) + Cos[Pi \[Nu]] ChebyshevT[\[Nu], -Subscript[z, 0]] (-2 I I^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)] + (1/(1 + Subscript[z, 0]))^((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) (1 + Subscript[z, 0])^((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)])) + (((\[Nu] Sin[Pi \[Nu]])/Sqrt[1 - Subscript[z, 0]^2]) (1/(1 + Subscript[z, 0]))^((1/2) Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)]) (1 + Subscript[z, 0])^ ((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]) ChebyshevT[\[Nu], -Subscript[z, 0]] - \[Nu] Cos[Pi \[Nu]] ChebyshevU[\[Nu] - 1, -Subscript[z, 0]] (-2 I I^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)] + (1/(1 + Subscript[z, 0]))^((1/2) Floor[Arg[z - Subscript[z, 0]]/ (2 Pi)]) (1 + Subscript[z, 0])^ ((1/2) Floor[Arg[z - Subscript[z, 0]]/(2 Pi)]))) (z - Subscript[z, 0]) + O[(z - Subscript[z, 0])^2])










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