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Statements
E
(
ϕ
,
k
)
=
k
′
2
R
F
(
c
-
1
,
c
-
k
2
,
c
)
+
1
3
k
2
k
′
2
R
D
(
c
-
1
,
c
,
c
-
k
2
)
+
k
2
(
c
-
1
)
/
(
c
(
c
-
k
2
)
)
,
elliptic-integral-second-kind-E
italic-ϕ
𝑘
superscript
superscript
𝑘
′
2
Carlson-integral-RF
𝑐
1
𝑐
superscript
𝑘
2
𝑐
1
3
superscript
𝑘
2
superscript
superscript
𝑘
′
2
Carlson-integral-RD
𝑐
1
𝑐
𝑐
superscript
𝑘
2
superscript
𝑘
2
𝑐
1
𝑐
𝑐
superscript
𝑘
2
{\displaystyle{\displaystyle E\left(\phi,k\right)={k^{\prime}}^{2}R_{F}\left(c%
-1,c-k^{2},c\right)+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(c-1,c,c-k^{2}%
\right)+k^{2}\sqrt{(c-1)/(c(c-k^{2}))},}}
c
>
k
2
𝑐
superscript
𝑘
2
{\displaystyle{\displaystyle c>k^{2}}}
R
D
(
x
,
y
,
z
)
Carlson-integral-RD
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
R
F
(
x
,
y
,
z
)
Carlson-integral-RF
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
E
(
ϕ
,
k
)
elliptic-integral-second-kind-E
italic-ϕ
𝑘
{\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
Identifiers
