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:28.23.E11 - MaRDI portal
Statements
Ms
2
m
+
1
(
j
)
(
z
,
h
)
=
(
-
1
)
m
(
se
2
m
+
1
(
1
2
π
,
h
2
)
)
-
1
∑
ℓ
=
0
∞
B
2
ℓ
+
1
2
m
+
1
(
h
2
)
𝒞
2
ℓ
+
1
(
j
)
(
2
h
sinh
z
)
,
modified-Mathieu-Ms
𝑗
2
𝑚
1
𝑧
ℎ
superscript
1
𝑚
superscript
Mathieu-se
2
𝑚
1
1
2
𝜋
superscript
ℎ
2
1
superscript
subscript
ℓ
0
superscript
subscript
𝐵
2
ℓ
1
2
𝑚
1
superscript
ℎ
2
superscript
subscript
𝒞
2
ℓ
1
𝑗
2
ℎ
𝑧
{\displaystyle{\displaystyle{\mathrm{Ms}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m%
}\left(\mathrm{se}_{2m+1}\left(\tfrac{1}{2}\pi,h^{2}\right)\right)^{-1}\sum_{%
\ell=0}^{\infty}B_{2\ell+1}^{2m+1}(h^{2}){\cal C}_{2\ell+1}^{(j)}(2h\sinh z),}}
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}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
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)}}
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)}}}
B
m
(
q
)
subscript
𝐵
𝑚
𝑞
{\displaystyle{\displaystyle B_{m}(q)}}
Identifiers
