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