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Statements
U
(
1
2
μ
2
,
μ
t
2
)
∼
g
¯
(
μ
)
e
-
μ
2
ξ
¯
(
t
2
+
1
)
1
4
∑
s
=
0
∞
u
¯
s
(
t
)
(
t
2
+
1
)
3
2
s
1
μ
2
s
,
asymptotic-expansion
parabolic-U
1
2
superscript
𝜇
2
𝜇
𝑡
2
¯
𝑔
𝜇
superscript
𝑒
superscript
𝜇
2
¯
𝜉
superscript
superscript
𝑡
2
1
1
4
superscript
subscript
𝑠
0
subscript
¯
𝑢
𝑠
𝑡
superscript
superscript
𝑡
2
1
3
2
𝑠
1
superscript
𝜇
2
𝑠
{\displaystyle{\displaystyle U\left(\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)%
\sim\frac{\overline{g}(\mu)e^{-\mu^{2}{\overline{\xi}}}}{(t^{2}+1)^{\frac{1}{4%
}}}\sum_{s=0}^{\infty}\frac{\overline{u}_{s}(t)}{(t^{2}+1)^{\frac{3}{2}s}}%
\frac{1}{\mu^{2s}},}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
s
𝑠
{\displaystyle{\displaystyle s}}
ξ
¯
¯
𝜉
{\displaystyle{\displaystyle\overline{\xi}}}
u
¯
s
(
t
)
subscript
¯
𝑢
𝑠
𝑡
{\displaystyle{\displaystyle\overline{u}_{s}(t)}}
g
¯
(
μ
)
¯
𝑔
𝜇
{\displaystyle{\displaystyle\overline{g}(\mu)}}
u
s
(
t
)
subscript
𝑢
𝑠
𝑡
{\displaystyle{\displaystyle u_{s}(t)}}
Identifiers
