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Statements
2
(
k
2
-
α
2
)
Π
(
ϕ
,
α
2
,
k
)
=
ω
2
-
α
2
1
+
k
′
Π
(
ϕ
1
,
α
1
2
,
k
1
)
+
k
2
F
(
ϕ
,
k
)
-
(
1
+
k
′
)
α
1
2
R
C
(
c
1
,
c
1
-
α
1
2
)
,
2
superscript
𝑘
2
superscript
𝛼
2
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
superscript
𝜔
2
superscript
𝛼
2
1
superscript
𝑘
′
elliptic-integral-third-kind-Pi
subscript
italic-ϕ
1
superscript
subscript
𝛼
1
2
subscript
𝑘
1
superscript
𝑘
2
elliptic-integral-first-kind-F
italic-ϕ
𝑘
1
superscript
𝑘
′
superscript
subscript
𝛼
1
2
Carlson-integral-RC
subscript
𝑐
1
subscript
𝑐
1
superscript
subscript
𝛼
1
2
{\displaystyle{\displaystyle 2(k^{2}-\alpha^{2})\Pi\left(\phi,\alpha^{2},k%
\right)=\frac{\omega^{2}-\alpha^{2}}{1+k^{\prime}}\Pi\left(\phi_{1},\alpha_{1}%
^{2},k_{1}\right)+k^{2}F\left(\phi,k\right)-{(1+k^{\prime})\alpha_{1}^{2}R_{C}%
\left(c_{1},c_{1}-\alpha_{1}^{2}\right)},}}
R
C
(
x
,
y
)
Carlson-integral-RC
𝑥
𝑦
{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
F
(
ϕ
,
k
)
elliptic-integral-first-kind-F
italic-ϕ
𝑘
{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
Π
(
ϕ
,
α
2
,
k
)
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
{\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}%
\right)}}
ϕ
italic-ϕ
{\displaystyle{\displaystyle\phi}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
α
2
superscript
𝛼
2
{\displaystyle{\displaystyle\alpha^{2}}}
k
1
subscript
𝑘
1
{\displaystyle{\displaystyle k_{1}}}
ϕ
1
subscript
italic-ϕ
1
{\displaystyle{\displaystyle\phi_{1}}}
ω
𝜔
{\displaystyle{\displaystyle\omega}}
α
1
subscript
𝛼
1
{\displaystyle{\displaystyle\alpha_{1}}}
c
1
subscript
𝑐
1
{\displaystyle{\displaystyle c_{1}}}
Identifiers
