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