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Statements
U
(
a
,
z
)
=
Γ
(
1
2
-
a
)
2
π
i
e
-
1
4
z
2
∫
-
∞
(
0
+
)
e
z
t
-
1
2
t
2
t
a
-
1
2
d
t
,
parabolic-U
𝑎
𝑧
Euler-Gamma
1
2
𝑎
2
𝜋
𝑖
superscript
𝑒
1
4
superscript
𝑧
2
superscript
subscript
limit-from
0
superscript
𝑒
𝑧
𝑡
1
2
superscript
𝑡
2
superscript
𝑡
𝑎
1
2
𝑡
{\displaystyle{\displaystyle U\left(a,z\right)=\frac{\Gamma\left(\frac{1}{2}-a%
\right)}{2\pi i}e^{-\frac{1}{4}z^{2}}\int_{-\infty}^{(0+)}e^{zt-\frac{1}{2}t^{%
2}}t^{a-\frac{1}{2}}\mathrm{d}t,}}
-
π
<
ph
t
<
π
𝜋
phase
𝑡
𝜋
{\displaystyle{\displaystyle-\pi<\operatorname{ph}t<\pi}}
a
≠
1
2
,
3
2
,
5
2
,
…
𝑎
1
2
3
2
5
2
…
{\displaystyle{\displaystyle a\neq\frac{1}{2},\frac{3}{2},\frac{5}{2},\dots}}
-
π
<
ph
t
<
π
𝜋
ph
𝑡
𝜋
{\displaystyle{\displaystyle-\pi<\operatorname{ph}t<\pi}}
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}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\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}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
Identifiers
