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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 generic point z==z0 > For the function itself





http://functions.wolfram.com/08.04.06.0011.01









  


  










Input Form





EllipticE[z, m] == EllipticE[Subscript[z, 0], m] + Sqrt[1 - m Sin[Subscript[z, 0]]^2] (z - Subscript[z, 0]) + Sqrt[1 - m Sin[Subscript[z, 0]]^2] Sum[((I^(k - 1) Binomial[k - 3/2, k - 1])/k!) Sum[((((-1)^q Binomial[k - 1, q])/(1 - 2 q)) Sum[Binomial[q, j] m^j (2 - m)^(q - j) 2^(k - j - q - 1) Sum[Binomial[j, i] (2 i - j)^(k - 1) E^(2 (2 i - j) I Subscript[z, 0]) (z - Subscript[z, 0])^k, {i, 0, j}], {j, 0, q}])/(1 - m Sin[Subscript[z, 0]]^2)^q, {q, 1, k - 1}], {k, 2, 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





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