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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 > Special cases





http://functions.wolfram.com/07.14.06.0020.01









  


  










Input Form





GegenbauerC[\[Nu], 1/2, z] == (Sin[\[Nu] Pi]/Pi) (Log[(z + 1)/2] Hypergeometric2F1[-\[Nu], \[Nu] + 1, 1, (z + 1)/2] - Sum[((Pochhammer[-\[Nu], k] Pochhammer[\[Nu] + 1, k])/k!^2) (2 PolyGamma[k + 1] - PolyGamma[k - \[Nu]] - PolyGamma[k + \[Nu] + 1]) ((z + 1)/2)^k, {k, 0, Infinity}]) /; !(Element[\[Nu], Integers] && \[Nu] >= 0)










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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