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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[2,z,q] > Representations through equivalent functions > With related functions > Involving Weierstrass functions





http://functions.wolfram.com/09.02.27.0009.01









  


  








Input Form





EllipticTheta[2, z, q] == 2 q^(1/4) Product[1 - q^(2 n), {n, 1, Infinity}] Product[1 + q^(2 n), {n, 1, Infinity}]^2 Exp[-((2 Subscript[\[Eta], 1] Subscript[\[Omega], 1] z^2)/Pi^2)] WeierstrassSigma[1, (2 Subscript[\[Omega], 1] z)/Pi, {Subscript[g, 2], Subscript[g, 3]}] /; {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && Subscript[\[Eta], 1] == WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}] && q == Exp[Pi I (Subscript[\[Omega], 3]/Subscript[\[Omega], 1])]








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