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Statements
k
′
2
-
k
′
2
k
2
sn
z
1
sn
z
2
sn
z
3
sn
z
4
+
k
2
cn
z
1
cn
z
2
cn
z
3
cn
z
4
-
dn
z
1
dn
z
2
dn
z
3
dn
z
4
=
0
.
superscript
superscript
𝑘
′
2
superscript
superscript
𝑘
′
2
superscript
𝑘
2
Jacobi-elliptic-sn
subscript
𝑧
1
𝑘
Jacobi-elliptic-sn
subscript
𝑧
2
𝑘
Jacobi-elliptic-sn
subscript
𝑧
3
𝑘
Jacobi-elliptic-sn
subscript
𝑧
4
𝑘
superscript
𝑘
2
Jacobi-elliptic-cn
subscript
𝑧
1
𝑘
Jacobi-elliptic-cn
subscript
𝑧
2
𝑘
Jacobi-elliptic-cn
subscript
𝑧
3
𝑘
Jacobi-elliptic-cn
subscript
𝑧
4
𝑘
Jacobi-elliptic-dn
subscript
𝑧
1
𝑘
Jacobi-elliptic-dn
subscript
𝑧
2
𝑘
Jacobi-elliptic-dn
subscript
𝑧
3
𝑘
Jacobi-elliptic-dn
subscript
𝑧
4
𝑘
0
{\displaystyle{\displaystyle{k^{\prime}}^{2}-{k^{\prime}}^{2}k^{2}%
\operatorname{sn}z_{1}\operatorname{sn}z_{2}\operatorname{sn}z_{3}%
\operatorname{sn}z_{4}+k^{2}\operatorname{cn}z_{1}\operatorname{cn}z_{2}%
\operatorname{cn}z_{3}\operatorname{cn}z_{4}-\operatorname{dn}z_{1}%
\operatorname{dn}z_{2}\operatorname{dn}z_{3}\operatorname{dn}z_{4}=0.}}
cn
(
z
,
k
)
Jacobi-elliptic-cn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
dn
(
z
,
k
)
Jacobi-elliptic-dn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
sn
(
z
,
k
)
Jacobi-elliptic-sn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
