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EllipticK






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticK[z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/08.02.06.0022.01









  


  










Input Form





EllipticK[z] \[Proportional] EllipticK[x] - 2 I EllipticK[1 - x] Floor[Arg[-z + x]/(2 Pi)] + (1/(2 Pi)) (((2 I Pi)/((-1 + x) x)) Floor[Arg[-z + x]/(2 Pi)] (-EllipticE[1 - x] + EllipticK[1 - x] x) + MeijerG[{{-(1/2), -(1/2)}, {}}, {{0, -1}, {}}, 1 - x]) (z - x) + (1/(4 Pi)) (((I Pi)/((-1 + x)^2 x^2)) Floor[Arg[-z + x]/(2 Pi)] (-2 EllipticE[1 - x] + (4 EllipticE[1 - x] + EllipticK[1 - x]) x - 3 EllipticK[1 - x] x^2) + MeijerG[{{-(3/2), -(3/2)}, {}}, {{0, -2}, {}}, 1 - x]) (z - x)^2 + \[Ellipsis] /; (z -> x) && Element[x, Reals] && x > 1










Standard Form





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MathML Form







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</apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <ci> x </ci> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.