Associated Weierstrass sigma function: Transformations (formula 09.16.16.0012)

WeierstrassSigma

$Mathematica Notation$

Elliptic Functions

WeierstrassSigma[n,z,{g₂,g₃}]

Transformations

Related transformations

General fractions of half-periods

http://functions.wolfram.com/09.16.16.0012.01

Input Form

WeierstrassSigma[1, 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[1, z + ((2 k + 1 - n) Subscript[\[Omega], 1])/n, {Subscript[g, 2], Subscript[g, 3]}]/WeierstrassSigma[1, ((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

WeierstrassSigma[z,{g₂,g₃}]