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