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Statements
σ
(
z
)
=
2
ω
1
π
exp
(
η
1
z
2
2
ω
1
)
sin
(
π
z
2
ω
1
)
∏
n
=
1
∞
sin
(
π
(
2
n
ω
3
+
z
)
/
(
2
ω
1
)
)
sin
(
π
(
2
n
ω
3
-
z
)
/
(
2
ω
1
)
)
sin
2
(
π
n
ω
3
/
ω
1
)
.
Weierstrass-sigma-on-lattice
𝑧
𝕃
2
subscript
𝜔
1
𝜋
subscript
𝜂
1
superscript
𝑧
2
2
subscript
𝜔
1
𝜋
𝑧
2
subscript
𝜔
1
superscript
subscript
product
𝑛
1
𝜋
2
𝑛
subscript
𝜔
3
𝑧
2
subscript
𝜔
1
𝜋
2
𝑛
subscript
𝜔
3
𝑧
2
subscript
𝜔
1
2
𝜋
𝑛
subscript
𝜔
3
subscript
𝜔
1
{\displaystyle{\displaystyle\sigma\left(z\right)=\frac{2\omega_{1}}{\pi}\exp%
\left(\frac{\eta_{1}z^{2}}{2\omega_{1}}\right)\sin\left(\frac{\pi z}{2\omega_{%
1}}\right)\prod_{n=1}^{\infty}\frac{\sin\left(\pi(2n\omega_{3}+z)/(2\omega_{1}%
)\right)\sin\left(\pi(2n\omega_{3}-z)/(2\omega_{1})\right)}{{\sin^{2}}\left(%
\pi n\omega_{3}/\omega_{1}\right)}.}}
σ
(
z
)
Weierstrass-sigma-on-lattice
𝑧
𝕃
{\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
ω
1
subscript
𝜔
1
{\displaystyle{\displaystyle\omega_{1}}}
η
j
subscript
𝜂
𝑗
{\displaystyle{\displaystyle\eta_{j}}}
