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variants of this functions
EllipticE






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself





http://functions.wolfram.com/08.01.06.0031.01









  


  










Input Form





EllipticE[z] == Sqrt[-z] + (Log[-z]/Sqrt[-z]) Sum[((1/(k! (1 + k)!)) Pochhammer[-(1/2), 1 + k]^2)/z^k, {k, 0, Infinity}] + (1/Sqrt[-z]) (1/4 - (3/(64 z)) Sum[KroneckerDelta[i - 1], {i, 0, Infinity}] + Log[2] Sum[((1/(k! (1 + k)!)) Pochhammer[1/2, k]^2)/z^k, {k, 0, Infinity}] + (9/64) Sum[(1/((k + 2)!^2 (k + 3))) Pochhammer[5/2, k]^2 (1/(3 + k) + 2/(k + 1) + 2/(k + 2) - 4/(2 k + 3) - 4 Sum[1/i, {i, k + 1, 2 k + 1}]) z^(-k - 2), {k, 0, Infinity}]) /; Abs[z] > 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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