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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==0





http://functions.wolfram.com/08.06.06.0084.01









  


  










Input Form





EllipticPi[n, z, m] \[Proportional] Round[Re[z]/Pi] (Pi/Sqrt[1 - n] - ((Pi (-1 + Sqrt[1 - n]))/ (2 Sqrt[1 - n] n)) m - ((3 Pi)/(16 n^2)) (2 - 2/Sqrt[1 - n] + n) m^2 + \[Ellipsis]) + ArcTanh[Sqrt[-1 + n] Tan[z]]/Sqrt[-1 + n] + (1/(2 n)) (-z + ArcTanh[Sqrt[-1 + n] Tan[z]]/Sqrt[-1 + n]) m + ((3 (4 ArcTanh[Sqrt[-1 + n] Tan[z]] + Sqrt[-1 + n] (-2 (2 + n) z + n Sin[2 z])))/(32 Sqrt[-1 + n] n^2)) m^2 + \[Ellipsis] /; (m -> 0)










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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