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:14.15.E24 - MaRDI portal
Statements
π―
Ξ½
-
ΞΌ
β‘
(
x
)
=
1
(
Ξ½
+
1
2
)
1
/
4
β’
2
(
Ξ½
+
ΞΌ
)
/
2
β’
Ξ
β‘
(
1
2
β’
Ξ½
+
1
2
β’
ΞΌ
+
3
4
)
β’
(
ΞΆ
2
-
Ξ±
2
x
2
-
a
2
)
1
/
4
β’
(
U
β‘
(
ΞΌ
-
Ξ½
-
1
2
,
(
2
β’
Ξ½
+
1
)
1
/
2
β’
ΞΆ
)
+
O
β‘
(
Ξ½
-
2
/
3
)
β’
env
β’
U
β‘
(
ΞΌ
-
Ξ½
-
1
2
,
(
2
β’
Ξ½
+
1
)
1
/
2
β’
ΞΆ
)
)
,
Ferrers-Legendre-P-first-kind
π
π
π₯
1
superscript
π
1
2
1
4
superscript
2
π
π
2
Euler-Gamma
1
2
π
1
2
π
3
4
superscript
superscript
π
2
superscript
πΌ
2
superscript
π₯
2
superscript
π
2
1
4
parabolic-U
π
π
1
2
superscript
2
π
1
1
2
π
Big-O
superscript
π
2
3
envelope-Parabolic-U
π
π
1
2
superscript
2
π
1
1
2
π
{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{1}{%
\left(\nu+\frac{1}{2}\right)^{1/4}2^{(\nu+\mu)/2}\Gamma\left(\frac{1}{2}\nu+%
\frac{1}{2}\mu+\frac{3}{4}\right)}\left(\frac{\zeta^{2}-\alpha^{2}}{x^{2}-a^{2%
}}\right)^{1/4}\*\left(U\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}%
\zeta\right)+O\left(\nu^{-2/3}\right)\mathrm{env}\mskip-1.0mu U\left(\mu-\nu-%
\tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta\right)\right),}}
O
β‘
(
x
)
Big-O
π₯
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π―
Ξ½
ΞΌ
β‘
(
x
)
Ferrers-Legendre-P-first-kind
π
π
π₯
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
env
β’
U
β‘
(
c
,
x
)
envelope-Parabolic-U
π
π₯
{\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu U\left(\NVar{c},\NVar{x}%
\right)}}
U
β‘
(
a
,
z
)
parabolic-U
π
π§
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
x
π₯
{\displaystyle{\displaystyle x}}
ΞΌ
π
{\displaystyle{\displaystyle\mu}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
a
π
{\displaystyle{\displaystyle a}}
ΞΆ
π
{\displaystyle{\displaystyle\zeta}}
Ξ±
πΌ
{\displaystyle{\displaystyle\alpha}}
