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:14.18.E7 - MaRDI portal
Statements
(
x
-
y
)
∑
k
=
0
n
(
2
k
+
1
)
P
k
(
x
)
Q
k
(
y
)
=
(
n
+
1
)
(
P
n
+
1
(
x
)
Q
n
(
y
)
-
P
n
(
x
)
Q
n
+
1
(
y
)
)
-
1
.
𝑥
𝑦
superscript
subscript
𝑘
0
𝑛
2
𝑘
1
shorthand-Legendre-P-first-kind
𝑘
𝑥
shorthand-Legendre-Q-second-kind
𝑘
𝑦
𝑛
1
shorthand-Legendre-P-first-kind
𝑛
1
𝑥
shorthand-Legendre-Q-second-kind
𝑛
𝑦
shorthand-Legendre-P-first-kind
𝑛
𝑥
shorthand-Legendre-Q-second-kind
𝑛
1
𝑦
1
{\displaystyle{\displaystyle(x-y)\sum_{k=0}^{n}(2k+1)P_{k}\left(x\right)Q_{k}%
\left(y\right)=(n+1)\left(P_{n+1}\left(x\right)Q_{n}\left(y\right)-P_{n}\left(%
x\right)Q_{n+1}\left(y\right)\right)-1.}}
P
ν
(
z
)
=
P
ν
0
(
z
)
shorthand-Legendre-P-first-kind
𝜈
𝑧
Legendre-P-first-kind
0
𝜈
𝑧
{\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}%
\left(z\right)}}
Q
ν
(
z
)
=
Q
ν
0
(
z
)
shorthand-Legendre-Q-second-kind
𝜈
𝑧
Legendre-Q-second-kind
0
𝜈
𝑧
{\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}%
\left(z\right)}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
