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WeierstrassZetaHalfPeriodValues






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZetaHalfPeriodValues[{g2,g3}] > Representations through equivalent functions > With related functions > Involving elliptic integrals and modular functions





http://functions.wolfram.com/09.21.27.0004.01









  


  










Input Form





WeierstrassZetaHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] == {Sqrt[Subscript[e, 1] - Subscript[e, 3]] (EllipticE[m] - (Subscript[e, 1]/(Subscript[e, 1] - Subscript[e, 3])) EllipticK[m]), (1/Sqrt[Subscript[e, 1] - Subscript[e, 3]]) (EllipticK[m] Subscript[e, 1] + I EllipticK[1 - m] Subscript[e, 3] - (Subscript[e, 1] - Subscript[e, 3]) (EllipticE[m] - I EllipticE[1 - m])), (-I) Sqrt[Subscript[e, 1] - Subscript[e, 3]] (EllipticE[1 - m] + (Subscript[e, 3]/(Subscript[e, 1] - Subscript[e, 3])) EllipticK[1 - m])} /; m == ModularLambda[Subscript[\[Omega], 3]/Subscript[\[Omega], 1]]










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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