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Statements
Ψ
3
(
0
,
0
,
z
)
=
Γ
(
1
3
)
|
z
|
1
/
3
3
+
{
o
(
1
)
,
z
→
+
∞
,
2
π
5
1
/
4
(
3
|
z
|
)
3
/
4
(
cos
(
2
3
(
3
|
z
|
5
)
5
/
2
-
1
4
π
)
+
o
(
1
)
)
,
z
→
-
∞
.
canonical-integral
3
0
0
𝑧
Euler-Gamma
1
3
superscript
𝑧
1
3
3
cases
little-o
1
→
𝑧
2
𝜋
superscript
5
1
4
superscript
3
𝑧
3
4
2
3
superscript
3
𝑧
5
5
2
1
4
𝜋
little-o
1
→
𝑧
{\displaystyle{\displaystyle\Psi_{3}\left(0,0,z\right)=\frac{\Gamma\left(%
\tfrac{1}{3}\right)}{|z|^{1/3}\sqrt{3}}+\begin{cases}o\left(1\right),&z\to+%
\infty,\\
\dfrac{2\sqrt{\pi}5^{1/4}}{(3|z|)^{3/4}}\left(\cos\left(\dfrac{2}{3}\left(%
\dfrac{3|z|}{5}\right)^{5/2}-\dfrac{1}{4}\pi\right)+o\left(1\right)\right),&z%
\to-\infty.\end{cases}}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
Ψ
K
(
𝐱
)
canonical-integral
𝐾
𝐱
{\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
o
(
x
)
little-o
𝑥
{\displaystyle{\displaystyle o\left(\NVar{x}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
