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Statements
S
μ
,
ν
(
z
)
∼
z
μ
-
1
∑
k
=
0
∞
(
-
1
)
k
a
k
(
-
μ
,
ν
)
z
-
2
k
,
asymptotic-expansion
Lommel-S
𝜇
𝜈
𝑧
superscript
𝑧
𝜇
1
superscript
subscript
𝑘
0
superscript
1
𝑘
subscript
𝑎
𝑘
𝜇
𝜈
superscript
𝑧
2
𝑘
{\displaystyle{\displaystyle S_{{\mu},{\nu}}\left(z\right)\sim z^{\mu-1}\sum_{%
k=0}^{\infty}(-1)^{k}a_{k}(-\mu,\nu)z^{-2k},}}
|
ph
z
|
≤
π
-
δ
(
<
π
)
phase
𝑧
annotated
𝜋
𝛿
absent
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}
z
→
∞
→
𝑧
{\displaystyle{\displaystyle z\to\infty}}
|
ph
z
|
≤
π
-
δ
(
<
π
)
ph
𝑧
annotated
𝜋
𝛿
absent
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta(<\pi)}}
S
μ
,
ν
(
z
)
Lommel-S
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle S_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right%
)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
k
𝑘
{\displaystyle{\displaystyle k}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
a
k
(
μ
,
ν
)
subscript
𝑎
𝑘
𝜇
𝜈
{\displaystyle{\displaystyle a_{k}(\mu,\nu)}}
