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JacobiZeta




Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Representations through more general functions > Through Meijer G > Classical cases involving tan-1 in the arguments





http://functions.wolfram.com/08.07.26.0002.01









  


  








Input Form





JacobiZeta[ArcTan[z^(1/4)], 1 - 1/z] == (Sqrt[z] - 1)/(2 Sqrt[z]) - (1/(4 Pi)) MeijerG[{{0, 1}, {}}, {{-(1/2), 1/2}, {}}, z] - (EllipticE[1 - 1/z]/(4 Pi EllipticK[1 - 1/z])) MeijerG[{{1, 1}, {}}, {{1/2, 1/2}, {}}, z] /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]








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