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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 2F1





http://functions.wolfram.com/07.12.26.0088.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 3, z] == E^((1/2) I Pi (\[Mu] - \[Nu])) 2^(-1 + \[Mu]) Sqrt[Pi] (1 + z)^(\[Mu]/2) (-1 + z)^(\[Mu]/2) ((-((I Gamma[(1 + \[Mu] + \[Nu])/2])/Gamma[1 + (\[Nu] - \[Mu])/2])) Hypergeometric2F1[(\[Mu] - \[Nu])/2, (1 + \[Mu] + \[Nu])/2, 1/2, z^2] + ((2 z Gamma[1 + (\[Mu] + \[Nu])/2])/Gamma[(1 - \[Mu] + \[Nu])/2]) Hypergeometric2F1[(1 + \[Mu] - \[Nu])/2, (2 + \[Mu] + \[Nu])/2, 3/2, z^2]) /; !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