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variants of this functions
EllipticE




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z,m] > Representations through more general functions > Through other functions > Involving Weierstrass functions





http://functions.wolfram.com/08.04.26.0007.01









  


  








Input Form





EllipticE[z, m] == (1/EllipticK[m]) (EllipticE[m] EllipticF[z, m] + Subscript[\[Omega], 1] WeierstrassZeta[ (Subscript[\[Omega], 1] EllipticF[z, m])/EllipticK[m] - Subscript[\[Omega], 3], {Subscript[g, 2], Subscript[g, 3]}] + Subscript[\[Omega], 1] Subscript[\[Eta], 3]) - (Subscript[\[Omega], 1]/EllipticK[m]^2) EllipticF[z, m] Subscript[\[Eta], 1] /; m == InverseEllipticNomeQ[E^((I Pi Subscript[\[Omega], 3])/ Subscript[\[Omega], 1])] && {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && {Subscript[\[Eta], 1], Subscript[\[Eta], 3]} == {WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}], WeierstrassZeta[Subscript[\[Omega], 3], {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