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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==-csc-1(m1/2)+Pi u/;u ∈ Z





http://functions.wolfram.com/08.04.06.0033.01









  


  








Input Form





EllipticE[z, m] \[Proportional] (-Sqrt[m]) (EllipticE[1/m] + (-1 + 1/m) EllipticK[1/m]) + 2 u EllipticE[m] + ((2 Sqrt[2])/3) Sqrt[Sqrt[-1 + m] (z - Subscript[z, 0])] (z - Subscript[z, 0]) (1 - ((3 (-2 + m))/(20 Sqrt[-1 + m])) (z - Subscript[z, 0]) - ((-20 + 20 m + 3 m^2)/(224 (-1 + m))) (z - Subscript[z, 0])^2 - ((-2 + m)^3/(384 (-1 + m)^(3/2))) (z - Subscript[z, 0])^3 + \[Ellipsis]) /; (z -> Subscript[z, 0]) && Subscript[z, 0] == -ArcCsc[Sqrt[m]] + Pi u && Element[u, 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