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Statements
V
′
(
-
1
2
μ
2
,
μ
t
2
)
∼
(
2
π
)
1
2
μ
2
3
g
(
μ
)
ϕ
(
ζ
)
Γ
(
1
2
+
1
2
μ
2
)
(
Bi
(
μ
4
3
ζ
)
μ
4
3
∑
s
=
0
∞
C
s
(
ζ
)
μ
4
s
+
Bi
′
(
μ
4
3
ζ
)
∑
s
=
0
∞
D
s
(
ζ
)
μ
4
s
)
.
asymptotic-expansion
diffop
parabolic-V
1
1
2
superscript
𝜇
2
𝜇
𝑡
2
superscript
2
𝜋
1
2
superscript
𝜇
2
3
𝑔
𝜇
italic-ϕ
𝜁
Euler-Gamma
1
2
1
2
superscript
𝜇
2
Airy-Bi
superscript
𝜇
4
3
𝜁
superscript
𝜇
4
3
superscript
subscript
𝑠
0
subscript
𝐶
𝑠
𝜁
superscript
𝜇
4
𝑠
diffop
Airy-Bi
1
superscript
𝜇
4
3
𝜁
superscript
subscript
𝑠
0
subscript
𝐷
𝑠
𝜁
superscript
𝜇
4
𝑠
{\displaystyle{\displaystyle V'\left(-\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)%
\sim\frac{(2\pi)^{\frac{1}{2}}\mu^{\frac{2}{3}}g(\mu)}{\phi(\zeta)\Gamma\left(%
\tfrac{1}{2}+\tfrac{1}{2}\mu^{2}\right)}\*\left(\frac{\mathrm{Bi}\left(\mu^{%
\frac{4}{3}}\zeta\right)}{\mu^{\frac{4}{3}}}\sum_{s=0}^{\infty}\frac{C_{s}(%
\zeta)}{\mu^{4s}}+\mathrm{Bi}'\left(\mu^{\frac{4}{3}}\zeta\right)\sum_{s=0}^{%
\infty}\frac{D_{s}(\zeta)}{\mu^{4s}}\right).}}
Bi
(
z
)
Airy-Bi
𝑧
{\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
V
(
a
,
z
)
parabolic-V
𝑎
𝑧
{\displaystyle{\displaystyle V\left(\NVar{a},\NVar{z}\right)}}
s
𝑠
{\displaystyle{\displaystyle s}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
ϕ
(
ζ
)
italic-ϕ
𝜁
{\displaystyle{\displaystyle\phi(\zeta)}}
C
s
(
ζ
)
subscript
𝐶
𝑠
𝜁
{\displaystyle{\displaystyle C_{s}(\zeta)}}
D
s
(
ζ
)
subscript
𝐷
𝑠
𝜁
{\displaystyle{\displaystyle D_{s}(\zeta)}}
g
(
μ
)
𝑔
𝜇
{\displaystyle{\displaystyle g(\mu)}}
Identifiers
