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Statements
Bi
(
z
e
±
π
i
/
3
)
∼
2
π
e
±
π
i
/
6
z
1
/
4
(
cos
(
ζ
-
1
4
π
∓
1
2
i
ln
2
)
∑
k
=
0
∞
(
-
1
)
k
u
2
k
ζ
2
k
+
sin
(
ζ
-
1
4
π
∓
1
2
i
ln
2
)
∑
k
=
0
∞
(
-
1
)
k
u
2
k
+
1
ζ
2
k
+
1
)
,
asymptotic-expansion
Airy-Bi
𝑧
superscript
𝑒
plus-or-minus
𝜋
𝑖
3
2
𝜋
superscript
𝑒
plus-or-minus
𝜋
𝑖
6
superscript
𝑧
1
4
minus-or-plus
𝜁
1
4
𝜋
1
2
imaginary-unit
2
superscript
subscript
𝑘
0
superscript
1
𝑘
subscript
𝑢
2
𝑘
superscript
𝜁
2
𝑘
minus-or-plus
𝜁
1
4
𝜋
1
2
imaginary-unit
2
superscript
subscript
𝑘
0
superscript
1
𝑘
subscript
𝑢
2
𝑘
1
superscript
𝜁
2
𝑘
1
{\displaystyle{\displaystyle\mathrm{Bi}\left(ze^{\pm\pi i/3}\right)\mathrel{%
\sim}\sqrt{\frac{2}{\pi}}\frac{e^{\pm\pi i/6}}{z^{1/4}}\*\left(\cos\left(\zeta%
-\tfrac{1}{4}\pi\mp\tfrac{1}{2}\mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{%
k}\frac{u_{2k}}{\zeta^{2k}}+\sin\left(\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}%
\mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{2k+1}}{\zeta^{2k+1}}%
\right),}}
|
ph
z
|
≤
2
3
π
-
δ
phase
𝑧
2
3
𝜋
𝛿
{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi-\delta}}
Bi
(
z
)
Airy-Bi
𝑧
{\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
u
s
subscript
𝑢
𝑠
{\displaystyle{\displaystyle u_{s}}}
Identifiers
