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Statements
(
1
-
α
2
)
Π
(
α
2
,
k
)
=
(
ln
(
4
k
′
)
-
R
C
(
1
,
1
-
α
-
2
)
)
(
1
+
O
(
k
′
2
)
)
,
1
superscript
𝛼
2
complete-elliptic-integral-third-kind-Pi
superscript
𝛼
2
𝑘
4
superscript
𝑘
′
Carlson-integral-RC
1
1
superscript
𝛼
2
1
Big-O
superscript
superscript
𝑘
′
2
{\displaystyle{\displaystyle(1-\alpha^{2})\Pi\left(\alpha^{2},k\right)=\left(%
\ln\left(\frac{4}{k^{\prime}}\right)-R_{C}\left(1,1-\alpha^{-2}\right)\right)%
\*\left(1+O\left({k^{\prime}}^{2}\right)\right),}}
1
<
α
2
<
∞
1
superscript
𝛼
2
{\displaystyle{\displaystyle 1<\alpha^{2}<\infty}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
R
C
(
x
,
y
)
Carlson-integral-RC
𝑥
𝑦
{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
Π
(
α
2
,
k
)
complete-elliptic-integral-third-kind-Pi
superscript
𝛼
2
𝑘
{\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
k
𝑘
{\displaystyle{\displaystyle k}}
k
′
superscript
𝑘
′
{\displaystyle{\displaystyle k^{\prime}}}
α
2
superscript
𝛼
2
{\displaystyle{\displaystyle\alpha^{2}}}
Identifiers
