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Statements
∫
0
∞
e
-
p
t
Ai
(
-
t
)
d
t
=
1
3
e
p
3
/
3
(
Γ
(
1
3
,
1
3
p
3
)
Γ
(
1
3
)
+
Γ
(
2
3
,
1
3
p
3
)
Γ
(
2
3
)
)
,
superscript
subscript
0
superscript
𝑒
𝑝
𝑡
Airy-Ai
𝑡
𝑡
1
3
superscript
𝑒
superscript
𝑝
3
3
incomplete-Gamma
1
3
1
3
superscript
𝑝
3
Euler-Gamma
1
3
incomplete-Gamma
2
3
1
3
superscript
𝑝
3
Euler-Gamma
2
3
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-pt}\mathrm{Ai}\left(-t\right)%
\mathrm{d}t={\frac{1}{3}e^{p^{3}/3}\left(\frac{\Gamma\left(\tfrac{1}{3},\tfrac%
{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{1}{3}\right)}+\frac{\Gamma\left(\tfrac{%
2}{3},\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{2}{3}\right)}\right)},}}
ℜ
p
>
0
𝑝
0
{\displaystyle{\displaystyle\Re p>0}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
Γ
(
a
,
z
)
incomplete-Gamma
𝑎
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
p
𝑝
{\displaystyle{\displaystyle p}}
Identifiers
