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Statements
ζ
(
z
)
-
η
1
z
ω
1
-
π
2
ω
1
cot
(
π
z
2
ω
1
)
=
2
π
ω
1
∑
n
=
1
∞
q
2
n
1
-
q
2
n
sin
(
n
π
z
ω
1
)
.
Weierstrass-zeta-on-lattice
𝑧
𝕃
subscript
𝜂
1
𝑧
subscript
𝜔
1
𝜋
2
subscript
𝜔
1
𝜋
𝑧
2
subscript
𝜔
1
2
𝜋
subscript
𝜔
1
superscript
subscript
𝑛
1
superscript
𝑞
2
𝑛
1
superscript
𝑞
2
𝑛
𝑛
𝜋
𝑧
subscript
𝜔
1
{\displaystyle{\displaystyle\zeta\left(z\right)-\frac{\eta_{1}z}{\omega_{1}}-%
\frac{\pi}{2\omega_{1}}\cot\left(\frac{\pi z}{2\omega_{1}}\right)=\frac{2\pi}{%
\omega_{1}}\sum_{n=1}^{\infty}\frac{q^{2n}}{1-q^{2n}}\sin\left(\frac{n\pi z}{%
\omega_{1}}\right).}}
ζ
(
z
)
Weierstrass-zeta-on-lattice
𝑧
𝕃
{\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
q
𝑞
{\displaystyle{\displaystyle q}}
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}}}
