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DLMF:9.11.E16
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Formula:3621
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MaRDI QID
Q3621
Label: DLMF:9.11.E16
Digital Library of Mathematical Functions ID
9.11.E16
∫
-
∞
∞
Ai
3
(
t
)
d
t
=
Γ
2
(
1
3
)
4
π
2
,
superscript
subscript
Airy-Ai
3
𝑡
𝑡
Euler-Gamma
2
1
3
4
superscript
𝜋
2
{\displaystyle{\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{3}}\left(t% \right)\mathrm{d}t=\frac{{\Gamma^{2}}\left(\frac{1}{3}\right)}{4\pi^{2}},}}
Constraint(s)
Symbols List
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)}}
: gamma function
π
{\displaystyle{\displaystyle\pi}}
: the ratio of the circumference of a circle to its diameter
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
: differential of x
∫
{\displaystyle{\displaystyle\int}}
: integral
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