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:14.12.E5 - MaRDI portal
Statements
P
ν
-
μ
(
x
)
=
(
x
2
-
1
)
-
μ
/
2
Γ
(
μ
)
∫
1
x
P
ν
(
t
)
(
x
-
t
)
μ
-
1
d
t
,
Legendre-P-first-kind
𝜇
𝜈
𝑥
superscript
superscript
𝑥
2
1
𝜇
2
Euler-Gamma
𝜇
superscript
subscript
1
𝑥
Legendre-spherical-polynomial
𝜈
𝑡
superscript
𝑥
𝑡
𝜇
1
𝑡
{\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(x\right)=\frac{\left(x^{2}-1%
\right)^{-\mu/2}}{\Gamma\left(\mu\right)}\int_{1}^{x}P_{\nu}\left(t\right)(x-t%
)^{\mu-1}\mathrm{d}t,}}
ℜ
μ
>
0
𝜇
0
{\displaystyle{\displaystyle\Re\mu>0}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
ν
μ
(
z
)
Legendre-P-first-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
P
n
(
x
)
Legendre-spherical-polynomial
𝑛
𝑥
{\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
