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Statements
℘
(
z
)
-
e
1
=
(
π
θ
3
(
0
,
q
)
θ
4
(
0
,
q
)
θ
2
(
π
z
/
(
2
ω
1
)
,
q
)
2
ω
1
θ
1
(
π
z
/
(
2
ω
1
)
,
q
)
)
2
,
Weierstrass-P-on-lattice
𝑧
𝕃
Weierstrass-e-on-lattice
1
𝕃
superscript
𝜋
Jacobi-theta
3
0
𝑞
Jacobi-theta
4
0
𝑞
Jacobi-theta
2
𝜋
𝑧
2
subscript
𝜔
1
𝑞
2
subscript
𝜔
1
Jacobi-theta
1
𝜋
𝑧
2
subscript
𝜔
1
𝑞
2
{\displaystyle{\displaystyle\wp\left(z\right)-e_{1}=\left(\frac{\pi\theta_{3}%
\left(0,q\right)\theta_{4}\left(0,q\right)\theta_{2}\left(\pi z/(2\omega_{1}),%
q\right)}{2\omega_{1}\theta_{1}\left(\pi z/(2\omega_{1}),q\right)}\right)^{2},}}
θ
j
(
z
,
q
)
Jacobi-theta
𝑗
𝑧
𝑞
{\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
℘
(
z
)
Weierstrass-P-on-lattice
𝑧
𝕃
{\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}
e
j
Weierstrass-e-on-lattice
𝑗
𝕃
{\displaystyle{\displaystyle e_{\NVar{j}}}}
π
{\displaystyle{\displaystyle\pi}}
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
q
𝑞
{\displaystyle{\displaystyle q}}
z
𝑧
{\displaystyle{\displaystyle z}}
ω
1
subscript
𝜔
1
{\displaystyle{\displaystyle\omega_{1}}}
