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