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variants of this functions
EllipticPi




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,z,m] > Series representations > Generalized power series > Expansions at m==1





http://functions.wolfram.com/08.06.06.0093.01









  


  








Input Form





EllipticPi[n, z, m] \[Proportional] ((-1)^Round[Re[z]/Pi] ((Sqrt[n] ArcTanh[Sqrt[n] Sin[z]] - ArcTanh[Sin[z]])/ (n - 1)) + Round[Re[z]/Pi] ((-4 Log[2] + Sqrt[n] (-Log[1 - Sqrt[n]] + Log[1 + Sqrt[n]]))/ (-1 + n))) (1 + O[m - 1]) - Log[1 - m] (1/(1 - n)) Round[Re[z]/Pi] (1 + O[m - 1]) /; !Element[(Pi + 2 Re[z])/(4 Pi), Integers]








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