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variants of this functions
WeierstrassSigma






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[n,z,{g2,g3}] > Transformations > Related transformations > General fractions of half-periods





http://functions.wolfram.com/09.16.16.0013.01









  


  










Input Form





WeierstrassSigma[2, z, WeierstrassInvariants[{Subscript[\[Omega], 1]/n, Subscript[\[Omega], 3]}]] == Exp[((n - 1)/n) Subscript[\[Eta], 1] z + Sum[(z^2/2) WeierstrassP[(2 k Subscript[\[Omega], 1])/n, {Subscript[g, 2], Subscript[g, 3]}] - ((2 k + 1 - n) Subscript[\[Eta], 1] z)/n, {k, 1, n - 1}]] Product[WeierstrassSigma[2, z + ((2 k + 1 - n) Subscript[\[Omega], 1])/n, {Subscript[g, 2], Subscript[g, 3]}]/WeierstrassSigma[2, ((2 k + 1 - n) Subscript[\[Omega], 1])/n, {Subscript[g, 2], Subscript[g, 3]}], {k, 0, n - 1}] /; Element[n, Integers] && n > 0










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