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EllipticK






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticK[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/08.02.06.0019.01









  


  










Input Form





EllipticK[z] == (1/(2 Pi)) Sum[(1/k!) (-2 Pi I (-1)^k Floor[(Pi + Arg[1 - Subscript[z, 0]])/(2 Pi)] Floor[Arg[-z + Subscript[z, 0]]/(2 Pi)] Gamma[1/2 + k]^2 Hypergeometric2F1Regularized[1/2 + k, 1/2 + k, 1 + k, 1 - Subscript[z, 0]] + MeijerG[{{1/2 - k, 1/2 - k}, {}}, {{0, -k}, {}}, 1 - Subscript[z, 0]]) (z - Subscript[z, 0])^k, {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





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