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Statements
dc
(
2
z
,
k
)
=
dc
2
(
z
,
k
)
+
k
′
2
sc
2
(
z
,
k
)
nc
2
(
z
,
k
)
1
-
k
′
2
sc
4
(
z
,
k
)
,
Jacobi-elliptic-dc
2
𝑧
𝑘
Jacobi-elliptic-dc
2
𝑧
𝑘
superscript
superscript
𝑘
′
2
Jacobi-elliptic-sc
2
𝑧
𝑘
Jacobi-elliptic-nc
2
𝑧
𝑘
1
superscript
superscript
𝑘
′
2
Jacobi-elliptic-sc
4
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{dc}\left(2z,k\right)=\frac{{%
\operatorname{dc}^{2}}\left(z,k\right)+{k^{\prime}}^{2}{\operatorname{sc}^{2}}%
\left(z,k\right){\operatorname{nc}^{2}}\left(z,k\right)}{1-{k^{\prime}}^{2}{%
\operatorname{sc}^{4}}\left(z,k\right)},}}
dc
(
z
,
k
)
Jacobi-elliptic-dc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
nc
(
z
,
k
)
Jacobi-elliptic-nc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
sc
(
z
,
k
)
Jacobi-elliptic-sc
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
Identifiers
