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Statements
ℰ
(
x
,
k
)
=
1
θ
3
2
(
0
,
q
)
θ
4
(
ξ
,
q
)
d
d
ξ
θ
4
(
ξ
,
q
)
+
E
(
k
)
K
(
k
)
x
,
Jacobi-Epsilon
𝑥
𝑘
1
Jacobi-theta
3
2
0
𝑞
Jacobi-theta
4
𝜉
𝑞
derivative
𝜉
Jacobi-theta
4
𝜉
𝑞
complete-elliptic-integral-second-kind-E
𝑘
complete-elliptic-integral-first-kind-K
𝑘
𝑥
{\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=\frac{1}{{\theta_{3}^{%
2}}\left(0,q\right)\theta_{4}\left(\xi,q\right)}\frac{\mathrm{d}}{\mathrm{d}%
\xi}\theta_{4}\left(\xi,q\right)+\frac{E\left(k\right)}{K\left(k\right)}x,}}
ℰ
(
x
,
k
)
Jacobi-Epsilon
𝑥
𝑘
{\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
θ
j
(
z
,
q
)
Jacobi-theta
𝑗
𝑧
𝑞
{\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
K
(
k
)
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
E
(
k
)
complete-elliptic-integral-second-kind-E
𝑘
{\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
q
𝑞
{\displaystyle{\displaystyle q}}
x
𝑥
{\displaystyle{\displaystyle x}}
k
𝑘
{\displaystyle{\displaystyle k}}
Identifiers
