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WeierstrassZeta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.17.27.0009.01









  


  










Input Form





{WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}], WeierstrassZeta[Subscript[\[Omega], 3], {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]), (-I) Sqrt[Subscript[e, 1] - Subscript[e, 3]] (EllipticE[1 - m] + (Subscript[e, 3]/(Subscript[e, 1] - Subscript[e, 3])) EllipticK[1 - m])} /; m == InverseEllipticNomeQ[q] && {Subscript[e, 1], Subscript[e, 2], Subscript[e, 3]} == WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}]










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