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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/07.11.26.0006.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == ((2^(-2 - \[Nu]) Sqrt[Pi] Csc[Pi \[Mu]])/ Gamma[-\[Mu] - \[Nu]]) ((z - 1)^(-\[Nu] - 1)/(1 - z^2)^(\[Mu]/2)) (Gamma[-(1/2) - \[Nu]] (Cos[Pi \[Mu]] (1 + z)^\[Mu] + Csc[Pi (\[Mu] + \[Nu])] Sin[Pi (\[Mu] - \[Nu])] (-z - 1)^\[Mu]) Hypergeometric2F1[1 + \[Nu], 1 + \[Mu] + \[Nu], 2 (1 + \[Nu]), 2/(1 - z)] - ((2^(2 \[Nu] + 1) Gamma[1/2 + \[Nu]] Gamma[-\[Mu] - \[Nu]])/Gamma[1 - \[Mu] + \[Nu]]) (z - 1)^(2 \[Nu] + 1) ((-z - 1)^\[Mu] - Cos[Pi \[Mu]] (1 + z)^\[Mu]) Hypergeometric2F1[-\[Nu], \[Mu] - \[Nu], -2 \[Nu], 2/(1 - z)]) /; !Element[\[Mu], Integers] && !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)





2001-10-29





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