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DLMF:28.22.E4 - MaRDI portal
Statements
Ms
m
(
2
)
(
z
,
h
)
=
2
π
1
g
o
,
m
(
h
)
se
m
′
(
0
,
h
2
)
(
-
f
o
,
m
(
h
)
Se
m
(
z
,
h
2
)
-
2
π
S
m
(
h
2
)
Ge
m
(
z
,
h
2
)
)
.
modified-Mathieu-Ms
2
𝑚
𝑧
ℎ
2
𝜋
1
subscript
𝑔
𝑜
𝑚
ℎ
diffop
Mathieu-se
𝑚
1
0
superscript
ℎ
2
subscript
𝑓
𝑜
𝑚
ℎ
modified-Mathieu-Se
𝑚
𝑧
superscript
ℎ
2
2
𝜋
subscript
𝑆
𝑚
superscript
ℎ
2
modified-Mathieu-Ge
𝑚
𝑧
superscript
ℎ
2
{\displaystyle{\displaystyle{\mathrm{Ms}^{(2)}_{m}}\left(z,h\right)=\sqrt{%
\frac{2}{\pi}}\dfrac{1}{g_{\mathit{o},m}(h)\mathrm{se}_{m}'\left(0,h^{2}\right%
)}\*\left(-f_{\mathit{o},m}(h)\mathrm{Se}_{m}\left(z,h^{2}\right)-\dfrac{2}{%
\pi S_{m}(h^{2})}\mathrm{Ge}_{m}\left(z,h^{2}\right)\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}}
Ge
n
(
z
,
q
)
modified-Mathieu-Ge
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{Ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
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)}}
f
e
,
n
(
h
)
subscript
𝑓
𝑒
𝑛
ℎ
{\displaystyle{\displaystyle f_{\mathit{e},n}(h)}}
S
n
(
q
)
subscript
𝑆
𝑛
𝑞
{\displaystyle{\displaystyle S_{n}(q)}}
Identifiers