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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F~1





http://functions.wolfram.com/07.11.26.0028.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == ((1/2) Sin[Pi (\[Mu] - \[Nu])] Sin[Pi \[Nu]] Sin[Pi (\[Mu] + \[Nu])] Csc[Pi \[Mu]]^2 Gamma[1 + \[Mu] + \[Nu]] (Gamma[-\[Mu] - \[Nu]] (1 - z)^\[Mu] (Cos[Pi \[Mu]] Csc[Pi (\[Mu] - \[Nu])] + Csc[Pi \[Nu]]) Hypergeometric2F1Regularized[-\[Nu], 1 + \[Nu], 1 - \[Mu], (1 + z)/2] + Gamma[\[Mu] - \[Nu]] (1 + z)^\[Mu] (Cos[Pi \[Mu]] Csc[Pi \[Nu]] - Csc[Pi (\[Mu] + \[Nu])]) Hypergeometric2F1Regularized[-\[Nu], 1 + \[Nu], 1 + \[Mu], (1 + z)/2]))/(1 - z^2)^(\[Mu]/2) /; !Element[\[Mu], Integers]










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