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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 z==-1 > For the function itself > General case





http://functions.wolfram.com/07.14.06.0014.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] == ((Cos[Pi (\[Nu] + \[Lambda])] Sec[Pi \[Lambda]] Gamma[\[Nu] + 2 \[Lambda]])/ (Gamma[\[Nu] + 1] Gamma[2 \[Lambda]])) Sum[((Pochhammer[-\[Nu], k] Pochhammer[\[Nu] + 2 \[Lambda], k])/ (Pochhammer[1/2 + \[Lambda], k] k!)) ((z + 1)/2)^k, {k, 0, Infinity}] - ((2^(1/2 - \[Lambda]) Sin[\[Nu] Pi] Gamma[\[Lambda] - 1/2])/(Sqrt[Pi] Gamma[\[Lambda]])) (z + 1)^(1/2 - \[Lambda]) Sum[((Pochhammer[1/2 + \[Nu] + \[Lambda], k] Pochhammer[ 1/2 - \[Nu] - \[Lambda], k])/(Pochhammer[3/2 - \[Lambda], k] k!)) ((z + 1)/2)^k, {k, 0, Infinity}] /; Abs[(z + 1)/2] < 1 && !Element[\[Lambda] + 1/2, 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)





2001-10-29





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