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Statements
ζ
(
z
)
=
1
z
+
∫
0
∞
(
e
-
s
(
z
s
-
sinh
(
z
s
)
)
f
1
(
s
,
τ
)
-
e
i
τ
s
(
z
s
-
sin
(
z
s
)
)
f
2
(
s
,
τ
)
)
d
s
,
Weierstrass-zeta-on-lattice
𝑧
𝕃
1
𝑧
superscript
subscript
0
superscript
𝑒
𝑠
𝑧
𝑠
𝑧
𝑠
subscript
𝑓
1
𝑠
𝜏
superscript
𝑒
𝑖
𝜏
𝑠
𝑧
𝑠
𝑧
𝑠
subscript
𝑓
2
𝑠
𝜏
𝑠
{\displaystyle{\displaystyle\zeta\left(z\right)=\frac{1}{z}+\int_{0}^{\infty}%
\left(e^{-s}\left(zs-\sinh\left(zs\right)\right)f_{1}(s,\tau)-e^{i\tau s}\left%
(zs-\sin\left(zs\right)\right)f_{2}(s,\tau)\right)\mathrm{d}s,}}
ζ
(
z
)
Weierstrass-zeta-on-lattice
𝑧
𝕃
{\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
𝕃
𝕃
{\displaystyle{\displaystyle\mathbb{L}}}
z
𝑧
{\displaystyle{\displaystyle z}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
f
j
(
s
,
τ
)
subscript
𝑓
𝑗
𝑠
𝜏
{\displaystyle{\displaystyle f_{j}(s,\tau)}}
