Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:36.9.E8 - MaRDI portal
Statements
|
Ψ
(
H
)
(
x
,
y
,
z
)
|
2
=
8
π
2
(
2
9
)
1
/
3
∫
-
∞
∞
∫
-
∞
∞
Ai
(
(
4
3
)
1
/
3
(
x
+
z
v
+
3
u
2
)
)
Ai
(
(
4
3
)
1
/
3
(
y
+
z
u
+
3
v
2
)
)
d
u
d
v
.
superscript
hyperbolic-umbilic-canonical-integral
𝑥
𝑦
𝑧
2
8
superscript
𝜋
2
superscript
2
9
1
3
superscript
subscript
superscript
subscript
Airy-Ai
superscript
4
3
1
3
𝑥
𝑧
𝑣
3
superscript
𝑢
2
Airy-Ai
superscript
4
3
1
3
𝑦
𝑧
𝑢
3
superscript
𝑣
2
𝑢
𝑣
{\displaystyle{\displaystyle\left|\Psi^{(\mathrm{H})}\left(x,y,z\right)\right|%
^{2}=8\pi^{2}\left(\frac{2}{9}\right)^{1/3}\int_{-\infty}^{\infty}\int_{-%
\infty}^{\infty}\mathrm{Ai}\left(\left(\frac{4}{3}\right)^{1/3}(x+zv+3u^{2})%
\right)\mathrm{Ai}\left(\left(\frac{4}{3}\right)^{1/3}(y+zu+3v^{2})\right)%
\mathrm{d}u\mathrm{d}v.}}
Ai
(
z
)
Airy-Ai
𝑧
{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
Ψ
(
H
)
(
𝐱
)
hyperbolic-umbilic-canonical-integral
𝐱
{\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(\NVar{\mathbf{x}}\right)}}
∫
{\displaystyle{\displaystyle\int}}
y
𝑦
{\displaystyle{\displaystyle y}}
z
𝑧
{\displaystyle{\displaystyle z}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
