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Statements
Π
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ϕ
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α
2
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k
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+
Π
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ϕ
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k
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k
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Π
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k
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Π
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ϕ
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k
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F
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ϕ
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α
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ω
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c
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R
C
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c
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,
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝜔
2
𝑘
superscript
𝑘
2
superscript
𝛼
2
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝛼
2
𝑘
superscript
𝑘
2
superscript
𝜔
2
elliptic-integral-third-kind-Pi
italic-ϕ
superscript
𝜔
2
𝑘
superscript
𝑘
2
elliptic-integral-first-kind-F
italic-ϕ
𝑘
superscript
𝛼
2
superscript
𝜔
2
𝑐
1
Carlson-integral-RC
𝑐
𝑐
superscript
𝑘
2
𝑐
superscript
𝛼
2
𝑐
superscript
𝜔
2
{\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)+\Pi\left(\phi,%
\omega^{2},k\right)(k^{2}-\alpha^{2})\Pi\left(\phi,\alpha^{2},k\right)+(k^{2}-%
\omega^{2})\Pi\left(\phi,\omega^{2},k\right)=k^{2}F\left(\phi,k\right)-\alpha^%
{2}\omega^{2}\sqrt{c-1}R_{C}\left(c(c-k^{2}),(c-\alpha^{2})(c-\omega^{2})%
\right),}}
(
1
-
α
2
)
(
1
-
ω
2
)
=
1
-
k
2
1
superscript
𝛼
2
1
superscript
𝜔
2
1
superscript
𝑘
2
{\displaystyle{\displaystyle(1-\alpha^{2})(1-\omega^{2})=1-k^{2}}}
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}}
α
2
superscript
𝛼
2
{\displaystyle{\displaystyle\alpha^{2}}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
