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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 on branch cuts > For the function itself





http://functions.wolfram.com/07.14.06.0046.01









  


  










Input Form





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










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





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