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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > General characteristics > Poles and essential singularities > With respect to lambda





http://functions.wolfram.com/07.14.04.0007.01









  


  








Input Form





Residue[GegenbauerC[\[Nu], \[Lambda], z], {\[Lambda], -((\[Nu] + j)/2)}] == ((2^(\[Nu] + j) Sqrt[Pi] (-1)^j)/(\[Nu]! j! Gamma[-((\[Nu] + j)/2)])) Hypergeometric2F1Regularized[-j, -\[Nu], (1 - \[Nu] - j)/2, (1 - z)/2] /; Element[j, Integers] && j >= 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