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.E38 - MaRDI portal
Statements
α
^
n
,
m
(
s
)
=
1
2
π
∫
0
2
π
cos
t
se
n
(
t
,
h
2
)
se
m
(
t
,
h
2
)
d
t
=
(
-
1
)
p
2
i
π
se
n
′
(
0
,
h
2
)
se
m
′
(
0
,
h
2
)
h
Ds
2
(
n
,
m
,
0
)
.
superscript
subscript
^
𝛼
𝑛
𝑚
𝑠
1
2
𝜋
superscript
subscript
0
2
𝜋
𝑡
Mathieu-se
𝑛
𝑡
superscript
ℎ
2
Mathieu-se
𝑚
𝑡
superscript
ℎ
2
𝑡
superscript
1
𝑝
2
imaginary-unit
𝜋
diffop
Mathieu-se
𝑛
1
0
superscript
ℎ
2
diffop
Mathieu-se
𝑚
1
0
superscript
ℎ
2
ℎ
Mathieu-Ds
2
𝑛
𝑚
0
{\displaystyle{\displaystyle\widehat{\alpha}_{n,m}^{(s)}=\dfrac{1}{2\pi}\int_{%
0}^{2\pi}\cos t\mathrm{se}_{n}\left(t,h^{2}\right)\mathrm{se}_{m}\left(t,h^{2}%
\right)\mathrm{d}t=(-1)^{p}\dfrac{2}{\mathrm{i}\pi}\dfrac{\mathrm{se}_{n}'%
\left(0,h^{2}\right)\mathrm{se}_{m}'\left(0,h^{2}\right)}{h\mathrm{Ds}_{2}%
\left(n,m,0\right)}.}}
Ds
j
(
n
,
m
,
z
)
Mathieu-Ds
𝑗
𝑛
𝑚
𝑧
{\displaystyle{\displaystyle\mathrm{Ds}_{\NVar{j}}\left(\NVar{n},\NVar{m},%
\NVar{z}\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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
α
^
n
,
m
subscript
^
𝛼
𝑛
𝑚
{\displaystyle{\displaystyle\widehat{\alpha}_{n,m}}}
