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Statements
z
a
,
s
=
e
3
4
π
i
2
τ
s
(
1
-
i
a
λ
s
2
τ
s
+
2
a
2
λ
s
2
-
8
a
2
λ
s
+
4
a
2
+
3
16
τ
s
2
+
O
(
λ
s
3
τ
s
-
3
)
)
,
subscript
𝑧
𝑎
𝑠
superscript
𝑒
3
4
𝜋
𝑖
2
subscript
𝜏
𝑠
1
𝑖
𝑎
subscript
𝜆
𝑠
2
subscript
𝜏
𝑠
2
superscript
𝑎
2
superscript
subscript
𝜆
𝑠
2
8
superscript
𝑎
2
subscript
𝜆
𝑠
4
superscript
𝑎
2
3
16
superscript
subscript
𝜏
𝑠
2
Big-O
superscript
subscript
𝜆
𝑠
3
superscript
subscript
𝜏
𝑠
3
{\displaystyle{\displaystyle z_{a,s}=e^{\frac{3}{4}\pi i}\sqrt{2\tau_{s}}\left%
(1-\frac{ia\lambda_{s}}{2\tau_{s}}+\frac{2a^{2}\lambda_{s}^{2}-8a^{2}\lambda_{%
s}+4a^{2}+3}{16\tau_{s}^{2}}+O\left(\lambda_{s}^{3}\tau_{s}^{-3}\right)\right)%
,}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
s
𝑠
{\displaystyle{\displaystyle s}}
a
𝑎
{\displaystyle{\displaystyle a}}
τ
s
subscript
𝜏
𝑠
{\displaystyle{\displaystyle\tau_{s}}}
λ
s
subscript
𝜆
𝑠
{\displaystyle{\displaystyle\lambda_{s}}}
Identifiers
