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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Identities > Recurrence identities > Distant neighbors





http://functions.wolfram.com/07.11.17.0020.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == Subscript[\[ScriptCapitalC], n][\[Nu], \[Mu], z] LegendreQ[\[Nu], \[Mu] - n, 2, z] + ((-n - 1 + \[Mu]) (-n + \[Mu]) - \[Nu] (1 + \[Nu])) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Mu], z] LegendreQ[\[Nu], \[Mu] - n - 1, 2, z] /; Subscript[\[ScriptCapitalC], 0][\[Nu], \[Mu], z] == 1 && Subscript[\[ScriptCapitalC], 1][\[Nu], \[Mu], z] == (2 (1 - \[Mu]) z)/Sqrt[1 - z^2] && Subscript[\[ScriptCapitalC], n][\[Nu], \[Mu], z] == ((2 z (n - \[Mu]))/Sqrt[1 - z^2]) Subscript[\[ScriptCapitalC], n - 1][ \[Nu], \[Mu], z] + ((-n + \[Mu]) (1 - n + \[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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</ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> </apply> <ci> &#957; </ci> <ci> &#956; </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02