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Statements
S
n
m
(
j
)
(
z
,
γ
)
=
{
ψ
n
(
j
)
(
γ
z
)
+
O
(
z
-
2
e
|
ℑ
z
|
)
,
j
=
1
,
2
,
ψ
n
(
j
)
(
γ
z
)
(
1
+
O
(
z
-
1
)
)
,
j
=
3
,
4
.
radial-spheroidal-wave-S
𝑚
𝑗
𝑛
𝑧
𝛾
cases
superscript
subscript
𝜓
𝑛
𝑗
𝛾
𝑧
Big-O
superscript
𝑧
2
superscript
𝑒
𝑧
𝑗
1
2
superscript
subscript
𝜓
𝑛
𝑗
𝛾
𝑧
1
Big-O
superscript
𝑧
1
𝑗
3
4
{\displaystyle{\displaystyle S^{m(j)}_{n}\left(z,\gamma\right)=\begin{cases}%
\psi_{n}^{(j)}(\gamma z)+O\left(z^{-2}e^{|\Im z|}\right),&j=1,2,\\
\psi_{n}^{(j)}(\gamma z)\left(1+O\left(z^{-1}\right)\right),&j=3,4.\end{cases}}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
ℑ
absent
{\displaystyle{\displaystyle\Im}}
S
n
m
(
j
)
(
z
,
γ
)
radial-spheroidal-wave-S
𝑚
𝑗
𝑛
𝑧
𝛾
{\displaystyle{\displaystyle S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},%
\NVar{\gamma}\right)}}
z
𝑧
{\displaystyle{\displaystyle z}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
≥
m
𝑛
𝑚
{\displaystyle{\displaystyle n\geq m}}
ψ
k
(
j
)
(
z
)
superscript
subscript
𝜓
𝑘
𝑗
𝑧
{\displaystyle{\displaystyle\psi_{k}^{(j)}(z)}}
γ
2
superscript
𝛾
2
{\displaystyle{\displaystyle\gamma^{2}}}
Identifiers
