Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:28.28.E20 - MaRDI portal
Statements
2
π
∫
0
π
𝒞
2
ℓ
(
j
)
(
2
h
R
)
cos
(
2
ℓ
ϕ
)
ce
2
m
(
t
,
h
2
)
d
t
=
ε
ℓ
(
-
1
)
ℓ
+
m
A
2
ℓ
2
m
(
h
2
)
Mc
2
m
(
j
)
(
z
,
h
)
,
2
𝜋
superscript
subscript
0
𝜋
subscript
superscript
𝒞
𝑗
2
ℓ
2
ℎ
𝑅
2
ℓ
italic-ϕ
Mathieu-ce
2
𝑚
𝑡
superscript
ℎ
2
𝑡
subscript
𝜀
ℓ
superscript
1
ℓ
𝑚
subscript
superscript
𝐴
2
𝑚
2
ℓ
superscript
ℎ
2
modified-Mathieu-Mc
𝑗
2
𝑚
𝑧
ℎ
{\displaystyle{\displaystyle\dfrac{2}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{2%
\ell}(2hR)\cos\left(2\ell\phi\right)\mathrm{ce}_{2m}\left(t,h^{2}\right)%
\mathrm{d}t=\varepsilon_{\ell}(-1)^{\ell+m}A^{2m}_{2\ell}(h^{2}){\mathrm{Mc}^{%
(j)}_{2m}}\left(z,h\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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
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}}
j
𝑗
{\displaystyle{\displaystyle j}}
z
𝑧
{\displaystyle{\displaystyle z}}
𝒞
μ
(
j
)
superscript
subscript
𝒞
𝜇
𝑗
{\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
ϕ
(
z
,
t
)
italic-ϕ
𝑧
𝑡
{\displaystyle{\displaystyle\phi(z,t)}}
R
(
z
,
t
)
𝑅
𝑧
𝑡
{\displaystyle{\displaystyle R(z,t)}}
ε
ℓ
subscript
𝜀
ℓ
{\displaystyle{\displaystyle\varepsilon_{\ell}}}
A
m
(
q
)
subscript
𝐴
𝑚
𝑞
{\displaystyle{\displaystyle A_{m}(q)}}
Identifiers
