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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/07.12.26.0085.01









  


  








Input Form





LegendreQ[\[Nu], \[Mu], 3, z] == 2^(-1 - \[Nu]) E^(I Pi \[Mu]) (-1 + z)^(\[Mu]/2) (1 + z)^(-(\[Mu]/2) + \[Nu]) (Gamma[\[Mu]] ((z + 1)^\[Mu]/(z - 1)^\[Mu]) Hypergeometric2F1[-\[Nu], -\[Mu] - \[Nu], 1 - \[Mu], (z - 1)/(z + 1)] + Pochhammer[1 - \[Mu] + \[Nu], 2 \[Mu]] Gamma[-\[Mu]] Hypergeometric2F1[-\[Nu], \[Mu] - \[Nu], 1 + \[Mu], (z - 1)/(z + 1)]) /; !Element[\[Mu], Integers] && !IntervalMemberQ[Interval[{-Infinity, -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