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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==1 > For the function itself





http://functions.wolfram.com/08.01.06.0007.01









  


  








Input Form





EllipticE[z] == 2 - Hypergeometric2F1[-(1/2), -(1/2), 1, 1 - z] + (((z - 1) Log[1 - z])/4) Hypergeometric2F1[3/2, 1/2, 2, 1 - z] + ((z - 1)/2) Sum[(((1 + 2 k) Pochhammer[1/2, k]^2)/(k! (1 + k)!)) (PolyGamma[1/2 + k] - PolyGamma[k + 1]) (1 - z)^k, {k, 0, Infinity}] /; Abs[z - 1] < 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)





2001-10-29