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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/05.08.17.0012.01









  


  










Input Form





LaguerreL[n, \[Lambda], z] == Subscript[\[ScriptCapitalC], m][n, \[Lambda], z] LaguerreL[m + n, \[Lambda], z] - ((m + n + 1)/(m + \[Lambda] + n)) Subscript[\[ScriptCapitalC], m - 1][n, \[Lambda], z] LaguerreL[m + 1 + n, \[Lambda], z] /; Subscript[\[ScriptCapitalC], 0][n, \[Lambda], z] == 1 && Subscript[\[ScriptCapitalC], 1][n, \[Lambda], z] == (2 n + \[Lambda] + 3 - z)/(n + \[Lambda] + 1) && Subscript[\[ScriptCapitalC], m][n, \[Lambda], z] == ((1 + 2 m - z + \[Lambda] + 2 n)/(m + \[Lambda] + n)) Subscript[\[ScriptCapitalC], m - 1][n, \[Lambda], z] - ((m + n)/(m + \[Lambda] + n - 1)) 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