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Statements
ℰ
(
x
,
k
)
=
k
2
k
′
2
∫
0
x
sd
2
(
t
,
k
)
d
t
+
k
′
2
x
+
k
2
sn
(
x
,
k
)
cd
(
x
,
k
)
,
Jacobi-Epsilon
𝑥
𝑘
superscript
𝑘
2
superscript
superscript
𝑘
′
2
superscript
subscript
0
𝑥
Jacobi-elliptic-sd
2
𝑡
𝑘
𝑡
superscript
superscript
𝑘
′
2
𝑥
superscript
𝑘
2
Jacobi-elliptic-sn
𝑥
𝑘
Jacobi-elliptic-cd
𝑥
𝑘
{\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=k^{2}{k^{\prime}}^{2}%
\int_{0}^{x}{\operatorname{sd}^{2}}\left(t,k\right)\mathrm{d}t+{k^{\prime}}^{2%
}x+k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right),}}
ℰ
(
x
,
k
)
Jacobi-Epsilon
𝑥
𝑘
{\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
cd
(
z
,
k
)
Jacobi-elliptic-cd
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
sd
(
z
,
k
)
Jacobi-elliptic-sd
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
sn
(
z
,
k
)
Jacobi-elliptic-sn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
x
𝑥
{\displaystyle{\displaystyle x}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
