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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 Meijer G > Classical cases involving algebraic functions





http://functions.wolfram.com/07.11.26.0011.01









  


  










Input Form





(z + 1)^\[Nu] LegendreQ[\[Nu], \[Mu], 2, (1 - z)/(1 + z)] == ((Pi Csc[Pi \[Mu]])/(2 Gamma[-\[Nu]] Gamma[-\[Mu] - \[Nu]])) ((Sin[Pi (\[Mu] - \[Nu])]/Sin[Pi (\[Mu] + \[Nu])]) MeijerG[{{1 + \[Mu]/2 + \[Nu], 1 - \[Mu]/2 + \[Nu]}, {}}, {{\[Mu]/2}, {-\[Mu]/2}}, z] + Cos[Pi \[Mu]] MeijerG[{{1 + \[Mu]/2 + \[Nu], 1 - \[Mu]/2 + \[Nu]}, {}}, {{-\[Mu]/2}, {\[Mu]/2}}, z]) /; !Element[\[Nu], Integers] && !Element[\[Mu], Integers] && !IntervalMemberQ[Interval[{-Infinity, 0}], 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)





2001-10-29