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Statements
H
ν
(
2
)
(
z
)
∼
(
2
π
z
)
1
2
e
-
i
ω
∑
k
=
0
∞
(
-
i
)
k
a
k
(
ν
)
z
k
,
asymptotic-expansion
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
superscript
2
𝜋
𝑧
1
2
superscript
𝑒
𝑖
𝜔
superscript
subscript
𝑘
0
superscript
𝑖
𝑘
subscript
𝑎
𝑘
𝜈
superscript
𝑧
𝑘
{\displaystyle{\displaystyle{H^{(2)}_{\nu}}\left(z\right)\sim\left(\frac{2}{%
\pi z}\right)^{\frac{1}{2}}e^{-i\omega}\sum_{k=0}^{\infty}(-i)^{k}\frac{a_{k}(%
\nu)}{z^{k}},}}
-
2
π
+
δ
≤
ph
z
≤
π
-
δ
2
𝜋
𝛿
phase
𝑧
𝜋
𝛿
{\displaystyle{\displaystyle-2\pi+\delta\leq\operatorname{ph}z\leq\pi-\delta}}
H
ν
(
2
)
(
z
)
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
a
k
(
ν
)
subscript
𝑎
𝑘
𝜈
{\displaystyle{\displaystyle a_{k}(\nu)}}
ω
𝜔
{\displaystyle{\displaystyle\omega}}
Identifiers
