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Statements
ℰ
(
x
,
k
)
=
-
∫
0
x
(
ns
2
(
t
,
k
)
-
t
-
2
)
d
t
+
x
-
1
+
x
-
cn
(
x
,
k
)
ds
(
x
,
k
)
,
Jacobi-Epsilon
𝑥
𝑘
superscript
subscript
0
𝑥
Jacobi-elliptic-ns
2
𝑡
𝑘
superscript
𝑡
2
𝑡
superscript
𝑥
1
𝑥
Jacobi-elliptic-cn
𝑥
𝑘
Jacobi-elliptic-ds
𝑥
𝑘
{\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=-\int_{0}^{x}\left({%
\operatorname{ns}^{2}}\left(t,k\right)-t^{-2}\right)\mathrm{d}t+x^{-1}+x-%
\operatorname{cn}\left(x,k\right)\operatorname{ds}\left(x,k\right),}}
ℰ
(
x
,
k
)
Jacobi-Epsilon
𝑥
𝑘
{\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
cn
(
z
,
k
)
Jacobi-elliptic-cn
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
ds
(
z
,
k
)
Jacobi-elliptic-ds
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
ns
(
z
,
k
)
Jacobi-elliptic-ns
𝑧
𝑘
{\displaystyle{\displaystyle\operatorname{ns}\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}}
Identifiers
