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Statements
U
(
a
,
z
)
=
e
-
1
4
z
2
Γ
(
3
4
+
1
2
a
)
∫
0
∞
t
1
2
a
-
1
4
e
-
t
(
z
2
+
2
t
)
-
1
2
a
-
1
4
d
t
,
parabolic-U
𝑎
𝑧
superscript
𝑒
1
4
superscript
𝑧
2
Euler-Gamma
3
4
1
2
𝑎
superscript
subscript
0
superscript
𝑡
1
2
𝑎
1
4
superscript
𝑒
𝑡
superscript
superscript
𝑧
2
2
𝑡
1
2
𝑎
1
4
𝑡
{\displaystyle{\displaystyle U\left(a,z\right)=\frac{e^{-\frac{1}{4}z^{2}}}{%
\Gamma\left(\frac{3}{4}+\frac{1}{2}a\right)}\*\int_{0}^{\infty}t^{\frac{1}{2}a%
-\frac{1}{4}}e^{-t}\left(z^{2}+2t\right)^{-\frac{1}{2}a-\frac{1}{4}}\mathrm{d}%
t,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
ℜ
a
>
-
3
2
𝑎
3
2
{\displaystyle{\displaystyle\Re a>-\tfrac{3}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
U
(
a
,
z
)
parabolic-U
𝑎
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
Identifiers
