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