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:14.17.E12 - MaRDI portal
Statements
β«
-
1
1
π°
Ξ½
β‘
(
x
)
β’
π°
Ξ»
β‘
(
x
)
β’
d
x
=
(
(
Ο
β‘
(
Ξ½
+
1
)
-
Ο
β‘
(
Ξ»
+
1
)
)
β’
(
1
+
cos
β‘
(
Ξ½
β’
Ο
)
β’
cos
β‘
(
Ξ»
β’
Ο
)
)
+
1
2
β’
Ο
β’
sin
β‘
(
(
Ξ»
-
Ξ½
)
β’
Ο
)
)
(
Ξ»
-
Ξ½
)
β’
(
Ξ»
+
Ξ½
+
1
)
,
superscript
subscript
1
1
shorthand-Ferrers-Legendre-Q-first-kind
π
π₯
shorthand-Ferrers-Legendre-Q-first-kind
π
π₯
π₯
digamma
π
1
digamma
π
1
1
π
π
π
π
1
2
π
π
π
π
π
π
π
π
1
{\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{Q}_{\nu}\left(x\right)\mathsf%
{Q}_{\lambda}\left(x\right)\mathrm{d}x=\frac{\left((\psi\left(\nu+1\right)-%
\psi\left(\lambda+1\right))(1+\cos\left(\nu\pi\right)\cos\left(\lambda\pi%
\right))+\frac{1}{2}\pi\sin\left((\lambda-\nu)\pi\right)\right)}{(\lambda-\nu)%
(\lambda+\nu+1)},}}
Ξ»
β’
Β andΒ
β’
Ξ½
β
-
1
,
-
2
,
-
3
,
β¦
π
Β andΒ
π
1
2
3
β¦
{\displaystyle{\displaystyle\lambda\text{ and }\nu\neq-1,-2,-3,\dots}}
Ο
{\displaystyle{\displaystyle\pi}}
cos
β‘
z
π§
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
π₯
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
Ο
β‘
(
z
)
digamma
π§
{\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
β«
{\displaystyle{\displaystyle\int}}
π°
Ξ½
β‘
(
x
)
=
π°
Ξ½
0
β‘
(
x
)
shorthand-Ferrers-Legendre-Q-first-kind
π
π₯
Ferrers-Legendre-Q-first-kind
0
π
π₯
{\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=%
\mathsf{Q}^{0}_{\nu}\left(x\right)}}
sin
β‘
z
π§
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
π₯
{\displaystyle{\displaystyle x}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
Identifiers
