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Statements
Ψ
(
E
)
(
𝐱
)
=
2
π
/
3
exp
(
i
(
4
27
z
3
+
1
3
x
z
-
1
4
π
)
)
∫
∞
exp
(
-
7
π
i
/
12
)
∞
exp
(
π
i
/
12
)
exp
(
i
(
u
6
+
2
z
u
4
+
(
z
2
+
x
)
u
2
+
y
2
12
u
2
)
)
d
u
,
elliptic-umbilic-canonical-integral
𝐱
2
𝜋
3
𝑖
4
27
superscript
𝑧
3
1
3
𝑥
𝑧
1
4
𝜋
superscript
subscript
7
𝜋
𝑖
12
𝜋
𝑖
12
𝑖
superscript
𝑢
6
2
𝑧
superscript
𝑢
4
superscript
𝑧
2
𝑥
superscript
𝑢
2
superscript
𝑦
2
12
superscript
𝑢
2
𝑢
{\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(\mathbf{x}\right)=2\sqrt{%
\ifrac{\pi}{3}}\,\exp\left(i\left(\tfrac{4}{27}z^{3}+\tfrac{1}{3}xz-\tfrac{1}{%
4}\pi\right)\right)\int_{\infty\exp\left(-7\pi i/12\right)}^{\infty\exp\left(%
\pi i/12\right)}\exp\left(i\left(u^{6}+2zu^{4}+(z^{2}+x)u^{2}+\frac{y^{2}}{12u%
^{2}}\right)\right)\mathrm{d}u,}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
Ψ
(
E
)
(
𝐱
)
elliptic-umbilic-canonical-integral
𝐱
{\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(\NVar{\mathbf{x}}\right)}}
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
y
𝑦
{\displaystyle{\displaystyle y}}
z
𝑧
{\displaystyle{\displaystyle z}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
