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Statements
R
J
(
0
,
g
0
2
,
a
0
2
,
-
q
0
2
)
=
-
3
π
4
M
(
a
0
,
g
0
)
(
q
0
2
+
a
0
2
)
(
2
+
a
0
2
-
g
0
2
q
0
2
+
g
0
2
∑
n
=
0
∞
Q
n
)
,
Carlson-integral-RJ
0
superscript
subscript
𝑔
0
2
superscript
subscript
𝑎
0
2
superscript
subscript
𝑞
0
2
3
𝜋
4
arithmetic-geometric-mean
subscript
𝑎
0
subscript
𝑔
0
superscript
subscript
𝑞
0
2
superscript
subscript
𝑎
0
2
2
superscript
subscript
𝑎
0
2
superscript
subscript
𝑔
0
2
superscript
subscript
𝑞
0
2
superscript
subscript
𝑔
0
2
superscript
subscript
𝑛
0
subscript
𝑄
𝑛
{\displaystyle{\displaystyle R_{J}\left(0,g_{0}^{2},a_{0}^{2},-q_{0}^{2}\right%
)=\frac{-3\pi}{4M\left(a_{0},g_{0}\right)(q_{0}^{2}+a_{0}^{2})}\*\left(2+\frac%
{a_{0}^{2}-g_{0}^{2}}{q_{0}^{2}+g_{0}^{2}}\sum_{n=0}^{\infty}Q_{n}\right),}}
R
J
(
x
,
y
,
z
,
p
)
Carlson-integral-RJ
𝑥
𝑦
𝑧
𝑝
{\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}%
\right)}}
M
(
a
,
g
)
arithmetic-geometric-mean
𝑎
𝑔
{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}
π
{\displaystyle{\displaystyle\pi}}
n
𝑛
{\displaystyle{\displaystyle n}}
Q
n
subscript
𝑄
𝑛
{\displaystyle{\displaystyle Q_{n}}}
a
n
subscript
𝑎
𝑛
{\displaystyle{\displaystyle a_{n}}}
g
n
subscript
𝑔
𝑛
{\displaystyle{\displaystyle g_{n}}}
Identifiers
