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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.12.17.0014.01









  


  








Input Form





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