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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Identities > Recurrence identities > Distant neighbors > With respect to lambda





http://functions.wolfram.com/07.03.17.0014.01









  


  










Input Form





LaguerreL[\[Nu], \[Lambda], z] == Subscript[\[ScriptCapitalC], n][\[Nu], \[Lambda], z] LaguerreL[\[Nu], \[Lambda] + n, z] - (z/(n + \[Lambda] + \[Nu])) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Lambda], z] LaguerreL[\[Nu], \[Lambda] + n + 1, z] /; Subscript[\[ScriptCapitalC], 0][\[Nu], \[Lambda], z] == 1 && Subscript[\[ScriptCapitalC], 1][\[Nu], \[Lambda], z] == (1 + z + \[Lambda])/(1 + \[Lambda] + \[Nu]) && Subscript[\[ScriptCapitalC], n][\[Nu], \[Lambda], z] == ((n + z + \[Lambda])/(n + \[Lambda] + \[Nu])) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Lambda], z] - (z/(n + \[Lambda] + \[Nu] - 1)) Subscript[\[ScriptCapitalC], n - 2][ \[Nu], \[Lambda], z] && Element[n, Integers] && n > 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





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