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Statements
𝖰𝗌
n
m
(
x
,
γ
2
)
=
∑
k
=
-
∞
-
N
-
1
(
-
1
)
k
a
′
n
,
k
m
(
γ
2
)
𝖯
n
+
2
k
m
(
x
)
+
∑
k
=
-
N
∞
(
-
1
)
k
a
n
,
k
m
(
γ
2
)
𝖰
n
+
2
k
m
(
x
)
,
spheroidal-wave-on-cut-Qs
𝑚
𝑛
𝑥
superscript
𝛾
2
superscript
subscript
𝑘
𝑁
1
superscript
1
𝑘
subscript
superscript
superscript
𝑎
′
𝑚
𝑛
𝑘
superscript
𝛾
2
Ferrers-Legendre-P-first-kind
𝑚
𝑛
2
𝑘
𝑥
superscript
subscript
𝑘
𝑁
superscript
1
𝑘
subscript
superscript
𝑎
𝑚
𝑛
𝑘
superscript
𝛾
2
Ferrers-Legendre-Q-first-kind
𝑚
𝑛
2
𝑘
𝑥
{\displaystyle{\displaystyle\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right)=\sum_%
{k=-\infty}^{-N-1}(-1)^{k}{a^{\prime}}^{m}_{n,k}(\gamma^{2})\mathsf{P}^{m}_{n+%
2k}\left(x\right)+\sum_{k=-N}^{\infty}(-1)^{k}a^{m}_{n,k}(\gamma^{2})\mathsf{Q%
}^{m}_{n+2k}\left(x\right),}}
𝖯
ν
μ
(
x
)
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
𝖰
ν
μ
(
x
)
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\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}}}
a
n
,
k
m
(
γ
2
)
subscript
superscript
𝑎
𝑚
𝑛
𝑘
superscript
𝛾
2
{\displaystyle{\displaystyle a^{m}_{n,k}(\gamma^{2})}}
N
𝑁
{\displaystyle{\displaystyle N}}
Identifiers
