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Statements
E
(
k
)
=
π
2
M
(
1
,
k
′
)
(
a
0
2
-
∑
n
=
0
∞
2
n
-
1
c
n
2
)
=
K
(
k
)
(
a
1
2
-
∑
n
=
2
∞
2
n
-
1
c
n
2
)
,
complete-elliptic-integral-second-kind-E
𝑘
𝜋
2
arithmetic-geometric-mean
1
superscript
𝑘
′
superscript
subscript
𝑎
0
2
superscript
subscript
𝑛
0
superscript
2
𝑛
1
superscript
subscript
𝑐
𝑛
2
complete-elliptic-integral-first-kind-K
𝑘
superscript
subscript
𝑎
1
2
superscript
subscript
𝑛
2
superscript
2
𝑛
1
superscript
subscript
𝑐
𝑛
2
{\displaystyle{\displaystyle E\left(k\right)=\frac{\pi}{2M\left(1,k^{\prime}%
\right)}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right)=K\left(k%
\right)\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right),}}
g
0
=
k
′
subscript
𝑔
0
superscript
𝑘
′
{\displaystyle{\displaystyle g_{0}=k^{\prime}}}
M
(
a
,
g
)
arithmetic-geometric-mean
𝑎
𝑔
{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}
π
{\displaystyle{\displaystyle\pi}}
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)}}
n
𝑛
{\displaystyle{\displaystyle n}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
a
n
subscript
𝑎
𝑛
{\displaystyle{\displaystyle a_{n}}}
g
n
subscript
𝑔
𝑛
{\displaystyle{\displaystyle g_{n}}}
Identifiers
