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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,2,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself > Expansion at a point at the left half-plane branch cut





http://functions.wolfram.com/07.08.06.0055.01









  


  










Input Form





LegendreP[\[Nu], \[Mu], 2, z] == ((-(1/(Pi Gamma[-\[Mu] - \[Nu]] Gamma[1 - \[Mu] + \[Nu]]))) (x + 1)^((1/2) \[Mu]) Exp[Pi I \[Mu] Floor[Arg[z - x]/(2 Pi)]] ((2 Pi^2 I Floor[Arg[-x + z]/(2 Pi)] Hypergeometric2F1Regularized[ -\[Nu], 1 + \[Nu], 1 + \[Mu], (1 + x)/2])/ E^(I Pi \[Mu] Floor[Arg[-x + z]/(2 Pi)]) + (Sin[Pi \[Nu]] MeijerG[{{1 + \[Nu], -\[Nu]}, {}}, {{0, -\[Mu]}, {}}, (1 + x)/2])/E^(2 I Pi \[Mu] Floor[Arg[-x + z]/(2 Pi)])))/ (1 - x)^((1/2) \[Mu]) + O[z - x] /; Element[x, Reals] && x < -1










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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