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Statements
ΞΆ
β‘
(
z
|
π
3
)
-
ΞΆ
β‘
(
z
+
2
β’
i
β’
K
β²
β‘
|
π
3
)
-
ΞΆ
β‘
(
2
β’
i
β’
K
β²
β‘
|
π
3
)
=
cs
β‘
(
z
,
k
)
.
Weierstrass-zeta-on-lattice
π§
subscript
π
3
Weierstrass-zeta-on-lattice
π§
2
imaginary-unit
complementary-complete-elliptic-integral-first-kind-K
π
subscript
π
3
Weierstrass-zeta-on-lattice
2
imaginary-unit
complementary-complete-elliptic-integral-first-kind-K
π
subscript
π
3
Jacobi-elliptic-cs
π§
π
{\displaystyle{\displaystyle\zeta\left(z|\mathbb{L}_{\mspace{1.0mu }3}\right)-%
\zeta\left(z+2\mathrm{i}{K^{\prime}}|\mathbb{L}_{\mspace{1.0mu }3}\right)-%
\zeta\left(2\mathrm{i}{K^{\prime}}|\mathbb{L}_{\mspace{1.0mu }3}\right)=%
\operatorname{cs}\left(z,k\right).}}
cs
β‘
(
z
,
k
)
Jacobi-elliptic-cs
π§
π
{\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
ΞΆ
β‘
(
z
)
Weierstrass-zeta-on-lattice
π§
π
{\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
K
β²
β‘
(
k
)
complementary-complete-elliptic-integral-first-kind-K
π
{\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
π
π
{\displaystyle{\displaystyle\mathbb{L}}}
z
π§
{\displaystyle{\displaystyle z}}
k
π
{\displaystyle{\displaystyle k}}
Identifiers
