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Statements
1
M
(
a
0
,
g
0
)
=
2
π
∫
0
π
/
2
d
θ
a
0
2
cos
2
θ
+
g
0
2
sin
2
θ
=
1
π
∫
0
∞
d
t
t
(
t
+
a
0
2
)
(
t
+
g
0
2
)
.
1
arithmetic-geometric-mean
subscript
𝑎
0
subscript
𝑔
0
2
𝜋
superscript
subscript
0
𝜋
2
𝜃
superscript
subscript
𝑎
0
2
2
𝜃
superscript
subscript
𝑔
0
2
2
𝜃
1
𝜋
superscript
subscript
0
𝑡
𝑡
𝑡
superscript
subscript
𝑎
0
2
𝑡
superscript
subscript
𝑔
0
2
{\displaystyle{\displaystyle\frac{1}{M\left(a_{0},g_{0}\right)}=\frac{2}{\pi}%
\int_{0}^{\pi/2}\frac{\mathrm{d}\theta}{\sqrt{a_{0}^{2}{\cos^{2}}\theta+g_{0}^%
{2}{\sin^{2}}\theta}}=\frac{1}{\pi}\int_{0}^{\infty}\frac{\mathrm{d}t}{\sqrt{t%
(t+a_{0}^{2})(t+g_{0}^{2})}}.}}
M
(
a
,
g
)
arithmetic-geometric-mean
𝑎
𝑔
{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
a
n
subscript
𝑎
𝑛
{\displaystyle{\displaystyle a_{n}}}
g
n
subscript
𝑔
𝑛
{\displaystyle{\displaystyle g_{n}}}
Identifiers
