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Statements
Ψ
(
E
)
(
0
,
0
,
z
)
=
Ψ
(
E
)
(
0
,
0
,
-
z
)
¯
=
2
π
π
z
27
exp
(
2
27
i
z
3
)
(
J
-
1
/
6
(
2
27
z
3
)
+
i
J
1
/
6
(
2
27
z
3
)
)
,
elliptic-umbilic-canonical-integral
0
0
𝑧
elliptic-umbilic-canonical-integral
0
0
𝑧
2
𝜋
𝜋
𝑧
27
2
27
𝑖
superscript
𝑧
3
Bessel-J
1
6
2
27
superscript
𝑧
3
𝑖
Bessel-J
1
6
2
27
superscript
𝑧
3
{\displaystyle{\displaystyle\Psi^{(\mathrm{E})}\left(0,0,z\right)=\overline{%
\Psi^{(\mathrm{E})}\left(0,0,-z\right)}\\
=2\pi\sqrt{\frac{\pi z}{27}}\exp\left(\frac{2}{27}iz^{3}\right)\*\left(J_{-1/6%
}\left(\frac{2}{27}z^{3}\right)+iJ_{1/6}\left(\frac{2}{27}z^{3}\right)\right),}}
z
≥
0
𝑧
0
{\displaystyle{\displaystyle z\geq 0}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
z
¯
𝑧
{\displaystyle{\displaystyle\overline{\NVar{z}}}}
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}}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
