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DLMF:28.22.E1 - MaRDI portal
Statements
Mc
m
(
1
)
(
z
,
h
)
=
2
π
1
g
e
,
m
(
h
)
ce
m
(
0
,
h
2
)
Ce
m
(
z
,
h
2
)
,
modified-Mathieu-Mc
1
𝑚
𝑧
ℎ
2
𝜋
1
subscript
𝑔
𝑒
𝑚
ℎ
Mathieu-ce
𝑚
0
superscript
ℎ
2
modified-Mathieu-Ce
𝑚
𝑧
superscript
ℎ
2
{\displaystyle{\displaystyle{\mathrm{Mc}^{(1)}_{m}}\left(z,h\right)=\sqrt{%
\dfrac{2}{\pi}}\dfrac{1}{g_{\mathit{e},m}(h)\mathrm{ce}_{m}\left(0,h^{2}\right%
)}\mathrm{Ce}_{m}\left(z,h^{2}\right),}}
ce
n
(
z
,
q
)
Mathieu-ce
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
Ce
ν
(
z
,
q
)
modified-Mathieu-Ce
𝜈
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}%
\right)}}
Mc
n
(
j
)
(
z
,
h
)
modified-Mathieu-Mc
𝑗
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z%
},\NVar{h}\right)}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
z
𝑧
{\displaystyle{\displaystyle z}}
g
e
,
n
(
h
)
subscript
𝑔
𝑒
𝑛
ℎ
{\displaystyle{\displaystyle g_{\mathit{e},n}(h)}}