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DLMF:30.13.E13 - MaRDI portal
Statements
w
2
âą
(
η
)
=
a
2
âą
đŻđ
n
m
âĄ
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η
,
Îł
2
)
+
b
2
âą
đ°đ
n
m
âĄ
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η
,
Îł
2
)
.
subscript
đ€
2
đ
subscript
đ
2
spheroidal-wave-on-cut-Ps
đ
đ
đ
superscript
đŸ
2
subscript
đ
2
spheroidal-wave-on-cut-Qs
đ
đ
đ
superscript
đŸ
2
{\displaystyle{\displaystyle w_{2}(\eta)=a_{2}\mathsf{Ps}^{m}_{n}\left(\eta,%
\gamma^{2}\right)+b_{2}\mathsf{Qs}^{m}_{n}\left(\eta,\gamma^{2}\right).}}
đŻđ
n
m
âĄ
(
x
,
Îł
2
)
spheroidal-wave-on-cut-Ps
đ
đ
đ„
superscript
đŸ
2
{\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},%
\NVar{\gamma^{2}}\right)}}
đ°đ
n
m
âĄ
(
x
,
Îł
2
)
spheroidal-wave-on-cut-Qs
đ
đ
đ„
superscript
đŸ
2
{\displaystyle{\displaystyle\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},%
\NVar{\gamma^{2}}\right)}}
m
đ
{\displaystyle{\displaystyle m}}
n
â„
m
đ
đ
{\displaystyle{\displaystyle n\geq m}}
b
j
subscript
đ
đ
{\displaystyle{\displaystyle b_{j}}}
η
đ
{\displaystyle{\displaystyle\eta}}
w
j
subscript
đ€
đ
{\displaystyle{\displaystyle w_{j}}}
Îł
2
=
Îș
2
âą
c
2
superscript
đŸ
2
superscript
đ
2
superscript
đ
2
{\displaystyle{\displaystyle\gamma^{2}=\kappa^{2}c^{2}}}
a
j
subscript
đ
đ
{\displaystyle{\displaystyle a_{j}}}