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Statements
∫
0
∞
e
-
3
4
t
2
t
-
a
-
3
2
U
(
a
,
t
)
d
t
=
2
1
4
+
1
2
a
Γ
(
-
a
-
1
2
)
cos
(
(
1
4
a
+
1
8
)
π
)
,
superscript
subscript
0
superscript
𝑒
3
4
superscript
𝑡
2
superscript
𝑡
𝑎
3
2
parabolic-U
𝑎
𝑡
𝑡
superscript
2
1
4
1
2
𝑎
Euler-Gamma
𝑎
1
2
1
4
𝑎
1
8
𝜋
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-\frac{3}{4}t^{2}}t^{-a-\frac{%
3}{2}}U\left(a,t\right)\mathrm{d}t=2^{\frac{1}{4}+\frac{1}{2}a}\Gamma\left(-a-%
\tfrac{1}{2}\right)\cos\left((\tfrac{1}{4}a+\tfrac{1}{8})\pi\right),}}
ℜ
a
<
-
1
2
𝑎
1
2
{\displaystyle{\displaystyle\Re a<-\tfrac{1}{2}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
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)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
a
𝑎
{\displaystyle{\displaystyle a}}
Identifiers
