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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,mu,2,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/05.07.26.0030.01









  


  










Input Form





LegendreP[n, \[Mu], 2, z] == (((2^(-2 - n) (Cos[2 Pi \[Mu]] - 1))/(Pi Sqrt[Pi])) (((Gamma[1 + \[Mu] + n]/(1 + 2 n)) Gamma[1/2 - n] (-z^2)^((1/2) (\[Mu] - n)) (-Csc[(1/2) Pi (\[Mu] - n)] + (Sqrt[-z^2]/z) Sec[(1/2) Pi (\[Mu] - n)]) Hypergeometric2F1[ (1/2) (1 - \[Mu] + n), (1/2) (2 - \[Mu] + n), 3/2 + n, 1/z^2])/z + 2^(2 n) Gamma[\[Mu] - n] Gamma[1/2 + n] (-z^2)^((1/2) (\[Mu] + n)) (-Csc[(1/2) Pi (\[Mu] + n)] + (Sqrt[-z^2]/z) Sec[(1/2) Pi (\[Mu] + n)]) Hypergeometric2F1[(1/2) (-\[Mu] - n), (1/2) (1 - \[Mu] - n), 1/2 - n, 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





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