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Statements
2
(
z
-
x
)
-
1
/
2
R
G
(
x
,
y
,
z
)
=
E
(
ϕ
,
k
)
+
(
cot
ϕ
)
2
F
(
ϕ
,
k
)
+
(
cot
ϕ
)
1
-
k
2
sin
2
ϕ
.
2
superscript
𝑧
𝑥
1
2
Carlson-integral-RG
𝑥
𝑦
𝑧
elliptic-integral-second-kind-E
italic-ϕ
𝑘
superscript
italic-ϕ
2
elliptic-integral-first-kind-F
italic-ϕ
𝑘
italic-ϕ
1
superscript
𝑘
2
2
italic-ϕ
{\displaystyle{\displaystyle 2(z-x)^{-1/2}R_{G}\left(x,y,z\right)=E\left(\phi,%
k\right)+(\cot\phi)^{2}F\left(\phi,k\right)+(\cot\phi)\sqrt{1-k^{2}{\sin^{2}}%
\phi}.}}
R
G
(
x
,
y
,
z
)
Carlson-integral-RG
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
F
(
ϕ
,
k
)
elliptic-integral-first-kind-F
italic-ϕ
𝑘
{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
E
(
ϕ
,
k
)
elliptic-integral-second-kind-E
italic-ϕ
𝑘
{\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
Identifiers
