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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F~1





http://functions.wolfram.com/07.12.26.0083.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 3, z] == (2^(\[Mu] - 1) E^(I Pi \[Mu]) Pi (-1 + z)^(\[Mu]/2) z^(1 - \[Mu] - \[Nu]) (1 + z)^(\[Mu]/2) ((-Sqrt[-(1/z^2)]) (Gamma[(1 + \[Mu] + \[Nu])/2]/ Gamma[(1/2) (2 - \[Mu] + \[Nu])]) Hypergeometric2F1Regularized[ (\[Mu] - \[Nu])/2, (1 + \[Mu] + \[Nu])/2, 1/2, z^2] + (Gamma[(2 + \[Mu] + \[Nu])/2]/Gamma[(1/2) (1 - \[Mu] + \[Nu])]) Hypergeometric2F1Regularized[(1 + \[Mu] - \[Nu])/2, 1 + (\[Mu] + \[Nu])/2, 3/2, z^2]))/ (-(1/z^2))^((1/2) (\[Mu] + \[Nu])) /; !IntervalMemberQ[Interval[{-Infinity, 0}], z] && !IntervalMemberQ[Interval[{1, Infinity}], 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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