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EllipticF






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticF[z,m] > Series representations > Generalized power series > Expansions at z==3Pi/2+2Pi u/;uZ && m>1





http://functions.wolfram.com/08.05.06.0050.01









  


  










Input Form





EllipticF[z, m] \[Proportional] ((-(1/Sqrt[m])) EllipticK[1/m] (I Sqrt[-(1/(z - Subscript[z, 0])^2)] (z - Subscript[z, 0]) + Sqrt[(z - Subscript[z, 0])^2]/ (z - Subscript[z, 0])) + EllipticK[m] (2 Round[Re[Subscript[z, 0]]/Pi] - Sqrt[I/(z - Subscript[z, 0])] Sqrt[(-I) (z - Subscript[z, 0])] + I Sqrt[-(1/(z - Subscript[z, 0])^2)] (z - Subscript[z, 0]) + Sqrt[(z - Subscript[z, 0])^2]/(z - Subscript[z, 0]))) (1 + O (z - Subscript[z, 0])) /; Subscript[z, 0] == (3 Pi)/2 + 2 Pi u && Element[u, Integers] && Element[m, Reals] && m > 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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