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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself





http://functions.wolfram.com/05.09.06.0029.01









  


  










Input Form





GegenbauerC[n, \[Lambda], z] == ((2^n Sqrt[Pi] Gamma[\[Lambda] + n/2])/(Gamma[\[Lambda]] Gamma[(1 - n)/2] n!)) Sum[((Pochhammer[-(n/2), k] Pochhammer[\[Lambda] + n/2, k])/ (Pochhammer[1/2, k] k!)) z^(2 k), {k, 0, Floor[n/2]}] + ((2^n Sqrt[Pi] z Gamma[\[Lambda] + (1 + n)/2])/ (Gamma[\[Lambda]] Gamma[1 - n/2] (n - 1)!)) Sum[((Pochhammer[(1 - n)/2, k] Pochhammer[\[Lambda] + (n + 1)/2, k])/ (Pochhammer[3/2, k] k!)) z^(2 k), {k, 0, Floor[(n - 1)/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





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