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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/05.09.16.0002.01









  


  








Input Form





GegenbauerC[m, \[Lambda], z] GegenbauerC[n, \[Lambda], z] == Sum[(1 - Mod[m + n + k, 2]) (((k + \[Lambda]) k! ((1/2) (m + n - k + 2 \[Lambda] - 2))! ((1/2) (m - n + k + 2 \[Lambda] - 2))! ((1/2) (-m + n + k + 2 \[Lambda] - 2))! ((1/2) (m + n + k + 4 \[Lambda] - 2))!)/(((1/2) (m + n - k))! ((1/2) (m - n + k))! ((1/2) (-m + n + k))! (\[Lambda] - 1)!^2 ((1/2) (m + n + k) + \[Lambda])! (k + 2 \[Lambda] - 1)!)), {k, Abs[m - n], m + n}] /; Element[GegenbauerC[k, \[Lambda], z] n, Integers] && n >= 0 && Element[m, Integers] && m >= 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)





2002-03-07