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Statements
θ
n
,
m
=
ϕ
m
+
(
(
α
2
-
1
4
)
1
-
ϕ
m
cot
ϕ
m
2
ϕ
m
-
1
4
(
α
2
-
β
2
)
tan
(
1
2
ϕ
m
)
)
1
ρ
2
+
ϕ
m
2
O
(
1
ρ
3
)
,
subscript
𝜃
𝑛
𝑚
subscript
italic-ϕ
𝑚
superscript
𝛼
2
1
4
1
subscript
italic-ϕ
𝑚
subscript
italic-ϕ
𝑚
2
subscript
italic-ϕ
𝑚
1
4
superscript
𝛼
2
superscript
𝛽
2
1
2
subscript
italic-ϕ
𝑚
1
superscript
𝜌
2
superscript
subscript
italic-ϕ
𝑚
2
Big-O
1
superscript
𝜌
3
{\displaystyle{\displaystyle\theta_{n,m}=\phi_{m}+\left(\left(\alpha^{2}-%
\tfrac{1}{4}\right)\frac{1-\phi_{m}\cot\phi_{m}}{2\phi_{m}}-\tfrac{1}{4}(%
\alpha^{2}-\beta^{2})\tan\left(\tfrac{1}{2}\phi_{m}\right)\right)\frac{1}{\rho%
^{2}}+\phi_{m}^{2}O\left(\frac{1}{\rho^{3}}\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
θ
n
,
m
subscript
𝜃
𝑛
𝑚
{\displaystyle{\displaystyle\theta_{n,m}}}
ϕ
m
subscript
italic-ϕ
𝑚
{\displaystyle{\displaystyle\phi_{m}}}
Identifiers
