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Statements
ρ
Π
(
ϕ
,
α
2
,
k
)
=
4
1
+
k
′
Π
(
ψ
1
,
α
1
2
,
k
1
)
+
(
ρ
-
1
)
F
(
ϕ
,
k
)
-
R
C
(
c
-
1
,
c
-
α
2
)
,
𝜌
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
4
1
superscript
𝑘
′
elliptic-integral-third-kind-Pi
subscript
𝜓
1
superscript
subscript
𝛼
1
2
subscript
𝑘
1
𝜌
1
elliptic-integral-first-kind-F
italic-ϕ
𝑘
Carlson-integral-RC
𝑐
1
𝑐
superscript
𝛼
2
{\displaystyle{\displaystyle\rho\Pi\left(\phi,\alpha^{2},k\right)=\frac{4}{1+k%
^{\prime}}\Pi\left(\psi_{1},\alpha_{1}^{2},k_{1}\right)+(\rho-1)F\left(\phi,k%
\right)-R_{C}\left(c-1,c-\alpha^{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}}}
ψ
1
subscript
𝜓
1
{\displaystyle{\displaystyle\psi_{1}}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
α
1
2
superscript
subscript
𝛼
1
2
{\displaystyle{\displaystyle\alpha_{1}^{2}}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
