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variants of this functions
EllipticE




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.04.06.0039.01









  


  








Input Form





EllipticE[z, m] \[Proportional] ((-EllipticE[ArcCsc[Sqrt[m]], m]) (I Sqrt[-(1/(z - Subscript[z, 0])^2)] (z - Subscript[z, 0]) + Sqrt[(z - Subscript[z, 0])^2]/ (z - Subscript[z, 0])) + EllipticE[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] == 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