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variants of this functions
EllipticE




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z,m] > Series representations > Other series representations > Expansions E(sin-1(z)|m) at m==1





http://functions.wolfram.com/08.04.06.0094.01









  


  








Input Form





EllipticE[ArcSin[z], m] == z + Sum[(((2 + 2 k - z^2) Pochhammer[1/2, k] z^(2 k + 1))/ (2 (1 + k)! (1 - z^2)^(k + 1)) - ((Pochhammer[1/2, k] z^(2 k + 1))/k!) Hypergeometric2F1[1/2 + k, 2 + k, 3/2 + k, z^2]) (m - 1)^(k + 1), {k, 0, Infinity}]








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