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:29.8.E2 - MaRDI portal
Statements
μ
w
(
z
1
)
w
(
z
2
)
w
(
z
3
)
=
∫
-
2
K
2
K
𝖯
ν
(
x
)
w
(
z
)
d
z
,
𝜇
𝑤
subscript
𝑧
1
𝑤
subscript
𝑧
2
𝑤
subscript
𝑧
3
superscript
subscript
2
complete-elliptic-integral-first-kind-K
𝑘
2
complete-elliptic-integral-first-kind-K
𝑘
shorthand-Ferrers-Legendre-P-first-kind
𝜈
𝑥
𝑤
𝑧
𝑧
{\displaystyle{\displaystyle\mu w(z_{1})w(z_{2})w(z_{3})=\int_{-2K}^{2K}%
\mathsf{P}_{\nu}\left(x\right)w(z)\mathrm{d}z,}}
K
(
k
)
complete-elliptic-integral-first-kind-K
𝑘
{\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
𝖯
ν
(
x
)
=
𝖯
ν
0
(
x
)
shorthand-Ferrers-Legendre-P-first-kind
𝜈
𝑥
Ferrers-Legendre-P-first-kind
0
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=%
\mathsf{P}^{0}_{\nu}\left(x\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
z
𝑧
{\displaystyle{\displaystyle z}}
k
𝑘
{\displaystyle{\displaystyle k}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
w
(
z
)
𝑤
𝑧
{\displaystyle{\displaystyle w(z)}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
