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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/07.07.06.0037.01









  


  










Input Form





LegendreP[\[Nu], z] \[Proportional] (Tan[Pi \[Nu]]/2) ((Gamma[-\[Nu]]/(2^\[Nu] Gamma[1 + \[Nu]])) ((1 + x)^\[Nu] Csc[Pi \[Nu]] + 2 I (-1 - x)^\[Nu] Floor[Arg[-x + z]/(2 Pi)]) Hypergeometric2F1Regularized[-\[Nu], -\[Nu], -2 \[Nu], 2/(1 + x)] - ((2^(1 + \[Nu]) Gamma[1 + \[Nu]])/ Gamma[-\[Nu]]) ((1 + x)^(-1 - \[Nu]) Csc[Pi \[Nu]] + 2 I (-1 - x)^(-1 - \[Nu]) Floor[Arg[-x + z]/(2 Pi)]) Hypergeometric2F1Regularized[1 + \[Nu], 1 + \[Nu], 2 + 2 \[Nu], 2/(1 + x)]) + 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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