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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Identities > Recurrence identities > Distant neighbors > With respect to n





http://functions.wolfram.com/05.09.17.0009.01









  


  










Input Form





GegenbauerC[n, \[Lambda], z] == Subscript[\[ScriptCapitalC], m][n, \[Lambda], z] GegenbauerC[n + m, \[Lambda], z] - ((m + n + 1)/(m + n - 1 + 2 \[Lambda])) Subscript[\[ScriptCapitalC], m - 1][n, \[Lambda], z] GegenbauerC[n + m + 1, \[Lambda], z] /; Subscript[\[ScriptCapitalC], 0][n, \[Lambda], z] == 1 && Subscript[\[ScriptCapitalC], 1][n, \[Lambda], z] == (2 (\[Lambda] + n + 1) z)/(2 \[Lambda] + n) && Subscript[\[ScriptCapitalC], m][n, \[Lambda], z] == ((2 z (m + n + \[Lambda]))/(m + n - 1 + 2 \[Lambda])) Subscript[\[ScriptCapitalC], m - 1][n, \[Lambda], z] - ((m + n)/(m + n - 2 + 2 \[Lambda])) Subscript[\[ScriptCapitalC], m - 2][ n, \[Lambda], z] && 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)





2007-05-02