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