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Statements
𝑄𝑠
n
m
(
x
±
i
0
,
γ
2
)
=
(
∓
i
)
m
(
𝖰𝗌
n
m
(
x
,
γ
2
)
∓
1
2
i
π
𝖯𝗌
n
m
(
x
,
γ
2
)
)
.
spheroidal-wave-Qs
𝑚
𝑛
plus-or-minus
𝑥
imaginary-unit
0
superscript
𝛾
2
superscript
minus-or-plus
imaginary-unit
𝑚
minus-or-plus
spheroidal-wave-on-cut-Qs
𝑚
𝑛
𝑥
superscript
𝛾
2
1
2
imaginary-unit
𝜋
spheroidal-wave-on-cut-Ps
𝑚
𝑛
𝑥
superscript
𝛾
2
{\displaystyle{\displaystyle\mathit{Qs}^{m}_{n}\left(x\pm\mathrm{i}0,\gamma^{2%
}\right)={(\mp\mathrm{i})^{m}\left(\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right%
)\mp\tfrac{1}{2}\mathrm{i}\pi\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)%
\right)}.}}
π
{\displaystyle{\displaystyle\pi}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
𝑄𝑠
n
m
(
z
,
γ
2
)
spheroidal-wave-Qs
𝑚
𝑛
𝑧
superscript
𝛾
2
{\displaystyle{\displaystyle\mathit{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{z},%
\NVar{\gamma^{2}}\right)}}
𝖯𝗌
n
m
(
x
,
γ
2
)
spheroidal-wave-on-cut-Ps
𝑚
𝑛
𝑥
superscript
𝛾
2
{\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},%
\NVar{\gamma^{2}}\right)}}
𝖰𝗌
n
m
(
x
,
γ
2
)
spheroidal-wave-on-cut-Qs
𝑚
𝑛
𝑥
superscript
𝛾
2
{\displaystyle{\displaystyle\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},%
\NVar{\gamma^{2}}\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
≥
m
𝑛
𝑚
{\displaystyle{\displaystyle n\geq m}}
γ
2
superscript
𝛾
2
{\displaystyle{\displaystyle\gamma^{2}}}
