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Statements
sn
2
(
z
,
k
)
=
1
k
2
(
1
-
E
K
)
-
2
π
2
k
2
K
2
∑
n
=
1
∞
n
q
n
1
-
q
2
n
cos
(
2
n
ζ
)
.
Jacobi-elliptic-sn
2
𝑧
𝑘
1
superscript
𝑘
2
1
complete-elliptic-integral-second-kind-E
𝑘
𝐾
2
superscript
𝜋
2
superscript
𝑘
2
superscript
𝐾
2
superscript
subscript
𝑛
1
𝑛
superscript
𝑞
𝑛
1
superscript
𝑞
2
𝑛
2
𝑛
𝜁
{\displaystyle{\displaystyle{\operatorname{sn}^{2}}\left(z,k\right)=\frac{1}{k%
^{2}}\left(1-\frac{E}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}%
\frac{nq^{n}}{1-q^{2n}}\cos\left(2n\zeta\right).}}
sn
(
z
,
k
)
Jacobi-elliptic-sn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
π
{\displaystyle{\displaystyle\pi}}
K
(
k
)
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
E
(
k
)
complete-elliptic-integral-second-kind-E
𝑘
{\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
q
𝑞
{\displaystyle{\displaystyle q}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
Identifiers
