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Statements
∫
0
∞
cos
(
2
x
t
)
𝐌
(
a
,
b
,
-
t
2
)
d
t
=
π
2
Γ
(
a
)
x
2
a
-
1
e
-
x
2
U
(
b
-
1
2
,
a
+
1
2
,
x
2
)
,
superscript
subscript
0
2
𝑥
𝑡
Kummer-confluent-hypergeometric-bold-M
𝑎
𝑏
superscript
𝑡
2
𝑡
𝜋
2
Euler-Gamma
𝑎
superscript
𝑥
2
𝑎
1
superscript
𝑒
superscript
𝑥
2
Kummer-confluent-hypergeometric-U
𝑏
1
2
𝑎
1
2
superscript
𝑥
2
{\displaystyle{\displaystyle\int_{0}^{\infty}\cos\left(2xt\right){\mathbf{M}}%
\left(a,b,-t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}}{2\Gamma\left(a\right)}x^{%
2a-1}e^{-x^{2}}U\left(b-\tfrac{1}{2},a+\tfrac{1}{2},x^{2}\right),}}
ℜ
a
>
0
𝑎
0
{\displaystyle{\displaystyle\Re a>0}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
𝐌
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-bold-M
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\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}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
