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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/07.14.06.0023.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] == (-((2^(1/2 - \[Lambda]) Cos[Pi (\[Nu] + \[Lambda])])/ ((1/2 - \[Lambda])! Sqrt[Pi] Gamma[\[Lambda]]))) (z + 1)^(1/2 - \[Lambda]) (Log[(1 + z)/2] + EulerGamma - PolyGamma[3/2 - \[Lambda]] + PolyGamma[1/2 - \[Lambda] - \[Nu]] + PolyGamma[1/2 + \[Lambda] + \[Nu]]) (1 + O[z + 1]) + ((2^(1 - 2 \[Lambda]) Cos[Pi (\[Nu] + \[Lambda])] (-(1/2) - \[Lambda])! Gamma[\[Nu] + 2 \[Lambda]])/(Sqrt[Pi] Gamma[\[Lambda]] Gamma[\[Nu] + 1])) (1 + O[z + 1]) /; Element[-(1/2) - \[Lambda], Integers] && -(1/2) - \[Lambda] >= 0 && !(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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