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Statements
K
n
m
(
γ
)
=
π
2
(
γ
2
)
m
+
1
(
-
1
)
m
a
n
,
1
2
(
m
-
n
+
1
)
-
m
(
γ
2
)
Γ
(
5
2
+
m
)
A
n
-
m
(
γ
2
)
(
d
𝖯𝗌
n
m
(
z
,
γ
2
)
/
d
z
|
z
=
0
)
,
superscript
subscript
𝐾
𝑛
𝑚
𝛾
𝜋
2
superscript
𝛾
2
𝑚
1
superscript
1
𝑚
superscript
subscript
𝑎
𝑛
1
2
𝑚
𝑛
1
𝑚
superscript
𝛾
2
Euler-Gamma
5
2
𝑚
superscript
subscript
𝐴
𝑛
𝑚
superscript
𝛾
2
evaluated-at
derivative
spheroidal-wave-on-cut-Ps
𝑚
𝑛
𝑧
superscript
𝛾
2
𝑧
𝑧
0
{\displaystyle{\displaystyle K_{n}^{m}(\gamma)=\frac{\sqrt{\pi}}{2}\left(\frac%
{\gamma}{2}\right)^{m+1}\*\frac{(-1)^{m}a_{n,\frac{1}{2}(m-n+1)}^{-m}(\gamma^{%
2})}{\Gamma\left(\frac{5}{2}+m\right)A_{n}^{-m}(\gamma^{2})(\left.\ifrac{%
\mathrm{d}\mathsf{Ps}^{m}_{n}(z,\gamma^{2})}{\mathrm{d}z}\right|_{z=0})},}}
n
-
m
𝑛
𝑚
{\displaystyle{\displaystyle n-m}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
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)}}
z
𝑧
{\displaystyle{\displaystyle z}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
≥
m
𝑛
𝑚
{\displaystyle{\displaystyle n\geq m}}
A
n
m
(
γ
2
)
superscript
subscript
𝐴
𝑛
𝑚
superscript
𝛾
2
{\displaystyle{\displaystyle A_{n}^{m}(\gamma^{2})}}
K
n
m
(
γ
)
superscript
subscript
𝐾
𝑛
𝑚
𝛾
{\displaystyle{\displaystyle K_{n}^{m}(\gamma)}}
γ
2
superscript
𝛾
2
{\displaystyle{\displaystyle\gamma^{2}}}
a
n
,
k
m
(
γ
2
)
subscript
superscript
𝑎
𝑚
𝑛
𝑘
superscript
𝛾
2
{\displaystyle{\displaystyle a^{m}_{n,k}(\gamma^{2})}}
Identifiers
