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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/07.09.26.0087.01









  


  










Input Form





LegendreP[\[Nu], \[Mu], 3, z] == (((2^(-2 - \[Nu]) (Cos[2 Pi \[Mu]] - Cos[2 Pi \[Nu]]))/(Pi Sqrt[Pi])) ((Gamma[1 + \[Mu] + \[Nu]]/(1 + 2 \[Nu])) Gamma[1/2 - \[Nu]] (1/z) (-z^2)^((1/2) (\[Mu] - \[Nu])) (-Csc[(1/2) Pi (\[Mu] - \[Nu])] + (Sqrt[-z^2]/z) Sec[(1/2) Pi (\[Mu] - \[Nu])]) Hypergeometric2F1[(1/2) (1 - \[Mu] + \[Nu]), (1/2) (2 - \[Mu] + \[Nu]), 3/2 + \[Nu], 1/z^2] + 2^(2 \[Nu]) Gamma[\[Mu] - \[Nu]] Gamma[1/2 + \[Nu]] (-z^2)^((1/2) (\[Mu] + \[Nu])) (-Csc[(1/2) Pi (\[Mu] + \[Nu])] + (Sqrt[-z^2]/z) Sec[(1/2) Pi (\[Mu] + \[Nu])]) Hypergeometric2F1[ (1/2) (-\[Mu] - \[Nu]), (1/2) (1 - \[Mu] - \[Nu]), 1/2 - \[Nu], 1/z^2]))/((-1 + z)^(\[Mu]/2) (1 + z)^(\[Mu]/2)) /; !IntervalMemberQ[Interval[{-1, 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)





2007-05-02





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