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Statements
A
n
(
-
z
)
=
{
2
p
/
π
cos
(
1
2
p
π
)
z
-
n
/
4
(
cos
(
ζ
-
1
4
π
)
+
e
|
ℑ
ζ
|
O
(
ζ
-
1
)
)
,
|
ph
z
|
≤
2
p
π
-
δ
,
n
odd
,
p
/
π
z
-
n
/
4
e
ζ
(
1
+
O
(
ζ
-
1
)
)
,
|
ph
z
|
≤
p
π
-
δ
,
n
even
,
ODE-generalized-Airy-A
𝑛
𝑧
cases
2
𝑝
𝜋
1
2
𝑝
𝜋
superscript
𝑧
𝑛
4
𝜁
1
4
𝜋
superscript
𝑒
𝜁
Big-O
superscript
𝜁
1
|
ph
z
|
≤
2
p
π
-
δ
,
n
odd
𝑝
𝜋
superscript
𝑧
𝑛
4
superscript
𝑒
𝜁
1
Big-O
superscript
𝜁
1
|
ph
z
|
≤
p
π
-
δ
,
n
even
{\displaystyle{\displaystyle A_{n}\left(-z\right)=\begin{cases}2\sqrt{p/\pi}%
\cos\left(\tfrac{1}{2}p\pi\right)z^{-n/4}\left(\cos\left(\zeta-\tfrac{1}{4}\pi%
\right)+e^{|\Im\zeta|}O\left(\zeta^{-1}\right)\right),&\text{$|\operatorname{%
ph}z|\leq 2p\pi-\delta$, $n$ odd},\\
\sqrt{p/\pi}z^{-n/4}e^{\zeta}\left(1+O\left(\zeta^{-1}\right)\right),&\text{$|%
\operatorname{ph}z|\leq p\pi-\delta$, $n$ even},\end{cases}}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
A
n
(
z
)
ODE-generalized-Airy-A
𝑛
𝑧
{\displaystyle{\displaystyle A_{\NVar{n}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
ℑ
absent
{\displaystyle{\displaystyle\Im}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
n
𝑛
{\displaystyle{\displaystyle n}}
p
𝑝
{\displaystyle{\displaystyle p}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
Identifiers
