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DLMF:28.22.E2 - MaRDI portal
Statements
Ms
m
(
1
)
(
z
,
h
)
=
2
π
1
g
o
,
m
(
h
)
se
m
′
(
0
,
h
2
)
Se
m
(
z
,
h
2
)
,
modified-Mathieu-Ms
1
𝑚
𝑧
ℎ
2
𝜋
1
subscript
𝑔
𝑜
𝑚
ℎ
diffop
Mathieu-se
𝑚
1
0
superscript
ℎ
2
modified-Mathieu-Se
𝑚
𝑧
superscript
ℎ
2
{\displaystyle{\displaystyle{\mathrm{Ms}^{(1)}_{m}}\left(z,h\right)=\sqrt{%
\dfrac{2}{\pi}}\frac{1}{g_{\mathit{o},m}(h)\mathrm{se}_{m}'\left(0,h^{2}\right%
)}\mathrm{Se}_{m}\left(z,h^{2}\right),}}
se
n
(
z
,
q
)
Mathieu-se
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
Ms
n
(
j
)
(
z
,
h
)
modified-Mathieu-Ms
𝑗
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z%
},\NVar{h}\right)}}
Se
ν
(
z
,
q
)
modified-Mathieu-Se
𝜈
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{Se}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}%
\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)}}
Identifiers