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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 nu





http://functions.wolfram.com/07.14.04.0009.01









  


  








Input Form





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