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Statements
ζ
(
z
)
=
π
2
4
ω
1
2
(
z
3
+
2
ω
1
π
cot
(
π
z
2
ω
1
)
-
8
(
z
-
ω
1
π
sin
(
π
z
ω
1
)
)
q
2
+
O
(
q
4
)
)
,
Weierstrass-zeta-on-lattice
𝑧
𝕃
superscript
𝜋
2
4
superscript
subscript
𝜔
1
2
𝑧
3
2
subscript
𝜔
1
𝜋
𝜋
𝑧
2
subscript
𝜔
1
8
𝑧
subscript
𝜔
1
𝜋
𝜋
𝑧
subscript
𝜔
1
superscript
𝑞
2
Big-O
superscript
𝑞
4
{\displaystyle{\displaystyle\zeta\left(z\right)=\frac{\pi^{2}}{4\omega_{1}^{2}%
}\left(\frac{z}{3}+\frac{2\omega_{1}}{\pi}\cot\left(\frac{\pi z}{2\omega_{1}}%
\right)-8\left(z-\frac{\omega_{1}}{\pi}\sin\left(\frac{\pi z}{\omega_{1}}%
\right)\right)q^{2}+O\left(q^{4}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\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}}
z
𝑧
{\displaystyle{\displaystyle z}}
ω
1
subscript
𝜔
1
{\displaystyle{\displaystyle\omega_{1}}}
