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Statements
(
℘
(
v
)
-
℘
(
w
)
)
(
℘
(
w
)
-
℘
(
u
)
)
(
℘
(
u
)
-
℘
(
v
)
)
∇
2
=
(
℘
(
w
)
-
℘
(
v
)
)
∂
2
∂
u
2
+
(
℘
(
u
)
-
℘
(
w
)
)
∂
2
∂
v
2
+
(
℘
(
v
)
-
℘
(
u
)
)
∂
2
∂
w
2
.
Weierstrass-P-on-lattice
𝑣
𝕃
Weierstrass-P-on-lattice
𝑤
𝕃
Weierstrass-P-on-lattice
𝑤
𝕃
Weierstrass-P-on-lattice
𝑢
𝕃
Weierstrass-P-on-lattice
𝑢
𝕃
Weierstrass-P-on-lattice
𝑣
𝕃
superscript
∇
2
Weierstrass-P-on-lattice
𝑤
𝕃
Weierstrass-P-on-lattice
𝑣
𝕃
partial-derivative
𝑢
2
Weierstrass-P-on-lattice
𝑢
𝕃
Weierstrass-P-on-lattice
𝑤
𝕃
partial-derivative
𝑣
2
Weierstrass-P-on-lattice
𝑣
𝕃
Weierstrass-P-on-lattice
𝑢
𝕃
partial-derivative
𝑤
2
{\displaystyle{\displaystyle\left(\wp\left(v\right)-\wp\left(w\right)\right)%
\left(\wp\left(w\right)-\wp\left(u\right)\right)\left(\wp\left(u\right)-\wp%
\left(v\right)\right)\nabla^{2}=\left(\wp\left(w\right)-\wp\left(v\right)%
\right)\frac{{\partial}^{2}}{{\partial u}^{2}}+\left(\wp\left(u\right)-\wp%
\left(w\right)\right)\frac{{\partial}^{2}}{{\partial v}^{2}}+\left(\wp\left(v%
\right)-\wp\left(u\right)\right)\frac{{\partial}^{2}}{{\partial w}^{2}}.}}
℘
(
z
)
Weierstrass-P-on-lattice
𝑧
𝕃
{\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
u
𝑢
{\displaystyle{\displaystyle u}}
v
𝑣
{\displaystyle{\displaystyle v}}
w
𝑤
{\displaystyle{\displaystyle w}}
