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Statements
W
(
1
2
μ
2
,
-
μ
t
2
)
∼
π
1
2
μ
1
3
l
(
μ
)
2
-
1
2
e
-
1
4
π
μ
2
ϕ
(
ζ
)
(
Ai
(
-
μ
4
3
ζ
)
∑
s
=
0
∞
(
-
1
)
s
A
s
(
ζ
)
μ
4
s
+
Ai
′
(
-
μ
4
3
ζ
)
μ
8
3
∑
s
=
0
∞
(
-
1
)
s
B
s
(
ζ
)
μ
4
s
)
,
asymptotic-expansion
parabolic-W
1
2
superscript
𝜇
2
𝜇
𝑡
2
superscript
𝜋
1
2
superscript
𝜇
1
3
𝑙
𝜇
superscript
2
1
2
superscript
𝑒
1
4
𝜋
superscript
𝜇
2
italic-ϕ
𝜁
Airy-Ai
superscript
𝜇
4
3
𝜁
superscript
subscript
𝑠
0
superscript
1
𝑠
subscript
𝐴
𝑠
𝜁
superscript
𝜇
4
𝑠
diffop
Airy-Ai
1
superscript
𝜇
4
3
𝜁
superscript
𝜇
8
3
superscript
subscript
𝑠
0
superscript
1
𝑠
subscript
𝐵
𝑠
𝜁
superscript
𝜇
4
𝑠
{\displaystyle{\displaystyle W\left(\tfrac{1}{2}\mu^{2},-\mu t\sqrt{2}\right)%
\sim\frac{\pi^{\frac{1}{2}}\mu^{\frac{1}{3}}l(\mu)}{2^{-\frac{1}{2}}e^{-\frac{%
1}{4}\pi\mu^{2}}}\phi(\zeta)\left(\mathrm{Ai}\left(-\mu^{\frac{4}{3}}\zeta%
\right)\sum_{s=0}^{\infty}(-1)^{s}\frac{A_{s}(\zeta)}{\mu^{4s}}+\frac{\mathrm{%
Ai}'\left(-\mu^{\frac{4}{3}}\zeta\right)}{\mu^{\frac{8}{3}}}\sum_{s=0}^{\infty%
}(-1)^{s}\frac{B_{s}(\zeta)}{\mu^{4s}}\right),}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
W
(
a
,
x
)
parabolic-W
𝑎
𝑥
{\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
s
𝑠
{\displaystyle{\displaystyle s}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
ϕ
(
ζ
)
italic-ϕ
𝜁
{\displaystyle{\displaystyle\phi(\zeta)}}
A
s
(
ζ
)
subscript
𝐴
𝑠
𝜁
{\displaystyle{\displaystyle A_{s}(\zeta)}}
B
s
(
ζ
)
subscript
𝐵
𝑠
𝜁
{\displaystyle{\displaystyle B_{s}(\zeta)}}
l
(
μ
)
𝑙
𝜇
{\displaystyle{\displaystyle l(\mu)}}
