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Statements
θ
1
′
(
z
,
q
)
θ
1
(
z
,
q
)
-
cot
z
=
4
sin
(
2
z
)
∑
n
=
1
∞
q
2
n
1
-
2
q
2
n
cos
(
2
z
)
+
q
4
n
=
4
∑
n
=
1
∞
q
2
n
1
-
q
2
n
sin
(
2
n
z
)
,
diffop
Jacobi-theta
1
1
𝑧
𝑞
Jacobi-theta
1
𝑧
𝑞
𝑧
4
2
𝑧
superscript
subscript
𝑛
1
superscript
𝑞
2
𝑛
1
2
superscript
𝑞
2
𝑛
2
𝑧
superscript
𝑞
4
𝑛
4
superscript
subscript
𝑛
1
superscript
𝑞
2
𝑛
1
superscript
𝑞
2
𝑛
2
𝑛
𝑧
{\displaystyle{\displaystyle\frac{\theta_{1}'\left(z,q\right)}{\theta_{1}\left%
(z,q\right)}-\cot z=4\sin\left(2z\right)\sum_{n=1}^{\infty}\frac{q^{2n}}{1-2q^%
{2n}\cos\left(2z\right)+q^{4n}}=4\sum_{n=1}^{\infty}\frac{q^{2n}}{1-q^{2n}}%
\sin\left(2nz\right),}}
θ
j
(
z
,
q
)
Jacobi-theta
𝑗
𝑧
𝑞
{\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
q
𝑞
{\displaystyle{\displaystyle q}}
Identifiers
