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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,2,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F~1





http://functions.wolfram.com/07.08.26.0035.01









  


  










Input Form





LegendreP[\[Nu], \[Mu], 2, z] == ((-((2^(-3 - \[Nu]) (Cos[2 Pi \[Mu]] - Cos[2 Pi \[Nu]]) Sec[Pi \[Nu]])/ Sqrt[Pi])) ((Gamma[1 + \[Mu] + \[Nu]] (-z^2)^((1/2) (\[Mu] - \[Nu])) (Csc[(1/2) Pi (\[Mu] - \[Nu])] - (Sqrt[-z^2]/z) Sec[(1/2) Pi (\[Mu] - \[Nu])]) Hypergeometric2F1Regularized[ (1/2) (1 - \[Mu] + \[Nu]), (1/2) (2 - \[Mu] + \[Nu]), 3/2 + \[Nu], 1/z^2])/z + 2^(1 + 2 \[Nu]) Gamma[\[Mu] - \[Nu]] (-z^2)^((1/2) (\[Mu] + \[Nu])) (Csc[(1/2) Pi (\[Mu] + \[Nu])] - (Sqrt[-z^2]/z) Sec[(1/2) Pi (\[Mu] + \[Nu])]) Hypergeometric2F1Regularized[(1/2) (-\[Mu] - \[Nu]), (1/2) (1 - \[Mu] - \[Nu]), 1/2 - \[Nu], 1/z^2]))/ (1 - z^2)^(\[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