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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Identities > Recurrence identities > Distant neighbors





http://functions.wolfram.com/07.09.17.0011.01









  


  










Input Form





LegendreP[\[Nu], \[Mu], 3, z] == Subscript[\[ScriptCapitalC], n][\[Nu], \[Mu], z] LegendreP[\[Nu], \[Mu] + n, 3, z] - (1/((n - 1 + \[Mu]) (n + \[Mu]) - \[Nu] (1 + \[Nu]))) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Mu], z] LegendreP[\[Nu], \[Mu] + n + 1, 3, z] /; Subscript[\[ScriptCapitalC], 0][\[Nu], \[Mu], z] == 1 && Subscript[\[ScriptCapitalC], 1][\[Nu], \[Mu], z] == (2 (\[Mu] + 1) z)/((\[Mu] (\[Mu] + 1) - \[Nu] (1 + \[Nu])) Sqrt[-1 - z] Sqrt[1 - z]) && Subscript[\[ScriptCapitalC], n][\[Nu], \[Mu], z] == ((2 z (n + \[Mu]))/(Sqrt[-1 - z] Sqrt[1 - z] ((n - 1 + \[Mu]) (n + \[Mu]) - \[Nu] (1 + \[Nu])))) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Mu], z] - (1/((n - 2 + \[Mu]) (n - 1 + \[Mu]) - \[Nu] (1 + \[Nu]))) Subscript[\[ScriptCapitalC], n - 2][\[Nu], \[Mu], 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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