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Statements
℘
(
z
+
ω
3
)
-
e
3
=
(
K
k
ω
1
)
2
sn
2
(
K
z
ω
1
,
k
)
.
Weierstrass-P-on-lattice
𝑧
subscript
𝜔
3
𝕃
Weierstrass-e-on-lattice
3
𝕃
superscript
complete-elliptic-integral-first-kind-K
𝑘
𝑘
subscript
𝜔
1
2
Jacobi-elliptic-sn
2
complete-elliptic-integral-first-kind-K
𝑘
𝑧
subscript
𝜔
1
𝑘
{\displaystyle{\displaystyle\wp\left(z+\omega_{3}\right)-e_{3}=\left(\frac{Kk}%
{\omega_{1}}\right)^{2}{\operatorname{sn}^{2}}\left(\frac{K\!z}{\omega_{1}},k%
\right).}}
sn
(
z
,
k
)
Jacobi-elliptic-sn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\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}}}}
K
(
k
)
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ω
1
subscript
𝜔
1
{\displaystyle{\displaystyle\omega_{1}}}
k
𝑘
{\displaystyle{\displaystyle k}}
Identifiers
