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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 2F1





http://functions.wolfram.com/07.11.26.0034.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == (((2^(-2 - \[Nu]) Sin[Pi (\[Mu] - \[Nu])])/(z Sqrt[Pi] (1 + 2 \[Nu]) Gamma[-\[Mu] - \[Nu]])) (-z^2)^((1/2) (-1 + \[Mu] - \[Nu])) (1 - 1/z^2)^\[Mu] (4^(1 + \[Nu]) z (-z^2)^\[Nu] Gamma[-\[Mu] - \[Nu]] Gamma[\[Mu] - \[Nu]] Gamma[3/2 + \[Nu]] Hypergeometric2F1[ (\[Mu] - \[Nu])/2, (1/2) (1 + \[Mu] - \[Nu]), 1/2 - \[Nu], 1/z^2] (z Cos[(1/2) Pi (\[Mu] + \[Nu])] - Sqrt[-z^2] Sin[(1/2) Pi (\[Mu] + \[Nu])]) + Pi Gamma[1/2 - \[Nu]] Hypergeometric2F1[(1/2) (1 + \[Mu] + \[Nu]), (1/2) (2 + \[Mu] + \[Nu]), 3/2 + \[Nu], 1/z^2] ((-Sqrt[-z^2]) Cot[(1/2) Pi (\[Mu] + \[Nu])] Csc[(1/2) Pi (\[Mu] - \[Nu])] + z Sec[(1/2) Pi (\[Mu] - \[Nu])] Tan[(1/2) Pi (\[Mu] + \[Nu])])))/(1 - z^2)^(\[Mu]/2) /; !IntervalMemberQ[Interval[{-1, 1}], z]










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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