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:19.16.E24 - MaRDI portal
Statements
R
-
a
(
𝐛
;
𝐳
)
=
z
1
a
′
-
b
1
B
(
b
1
,
a
′
-
b
1
)
∫
0
∞
t
b
1
-
1
(
t
+
z
1
)
-
a
′
R
-
a
(
𝐛
;
0
,
t
+
z
2
,
…
,
t
+
z
n
)
d
t
,
Carlson-integral-R
𝑎
𝐛
𝐳
superscript
subscript
𝑧
1
superscript
𝑎
′
subscript
𝑏
1
Euler-Beta
subscript
𝑏
1
superscript
𝑎
′
subscript
𝑏
1
superscript
subscript
0
superscript
𝑡
subscript
𝑏
1
1
superscript
𝑡
subscript
𝑧
1
superscript
𝑎
′
Carlson-integral-R
𝑎
𝐛
0
𝑡
subscript
𝑧
2
…
𝑡
subscript
𝑧
𝑛
𝑡
{\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{z_%
{1}^{a^{\prime}-b_{1}}}{\mathrm{B}\left(b_{1},a^{\prime}-b_{1}\right)}\int_{0}%
^{\infty}t^{b_{1}-1}(t+z_{1})^{-a^{\prime}}\*R_{-a}\left(\mathbf{b};0,t+z_{2},%
\dots,t+z_{n}\right)\mathrm{d}t,}}
a
+
a
′
>
b
1
>
0
𝑎
superscript
𝑎
′
subscript
𝑏
1
0
{\displaystyle{\displaystyle a+a^{\prime}>b_{1}>0}}
R
-
a
(
b
1
,
…
,
b
n
;
z
1
,
…
,
z
n
)
Carlson-integral-R
𝑎
subscript
𝑏
1
…
subscript
𝑏
𝑛
subscript
𝑧
1
…
subscript
𝑧
𝑛
{\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}%
};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
B
(
a
,
b
)
Euler-Beta
𝑎
𝑏
{\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
