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:16.17.E1 - MaRDI portal
Statements
G
p
,
q
m
,
n
(
z
;
𝐚
;
𝐛
)
=
G
p
,
q
m
,
n
(
z
;
a
1
,
…
,
a
p
b
1
,
…
,
b
q
)
=
1
2
π
i
∫
L
(
∏
ℓ
=
1
m
Γ
(
b
ℓ
-
s
)
∏
ℓ
=
1
n
Γ
(
1
-
a
ℓ
+
s
)
/
(
∏
ℓ
=
m
q
-
1
Γ
(
1
-
b
ℓ
+
1
+
s
)
∏
ℓ
=
n
p
-
1
Γ
(
a
ℓ
+
1
-
s
)
)
)
z
s
d
s
,
Meijer-G
𝑚
𝑛
𝑝
𝑞
𝑧
𝐚
𝐛
Meijer-G
𝑚
𝑛
𝑝
𝑞
𝑧
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
1
2
𝜋
imaginary-unit
subscript
𝐿
superscript
subscript
product
ℓ
1
𝑚
Euler-Gamma
subscript
𝑏
ℓ
𝑠
superscript
subscript
product
ℓ
1
𝑛
Euler-Gamma
1
subscript
𝑎
ℓ
𝑠
superscript
subscript
product
ℓ
𝑚
𝑞
1
Euler-Gamma
1
subscript
𝑏
ℓ
1
𝑠
superscript
subscript
product
ℓ
𝑛
𝑝
1
Euler-Gamma
subscript
𝑎
ℓ
1
𝑠
superscript
𝑧
𝑠
𝑠
{\displaystyle{\displaystyle{G^{m,n}_{p,q}}\left(z;\mathbf{a};\mathbf{b}\right%
)={G^{m,n}_{p,q}}\left(z;{a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}}\right)=%
\frac{1}{2\pi\mathrm{i}}\int_{L}\left({\textstyle\ifrac{\prod\limits_{\ell=1}^%
{m}\Gamma\left(b_{\ell}-s\right)\prod\limits_{\ell=1}^{n}\Gamma\left(1-a_{\ell%
}+s\right)}{\left(\prod\limits_{\ell=m}^{q-1}\Gamma\left(1-b_{\ell+1}+s\right)%
\prod\limits_{\ell=n}^{p-1}\Gamma\left(a_{\ell+1}-s\right)\right)}}\right)z^{s%
}\mathrm{d}s,}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
p
𝑝
{\displaystyle{\displaystyle p}}
q
𝑞
{\displaystyle{\displaystyle q}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
,
a
1
,
…
,
a
p
𝑎
subscript
𝑎
1
…
subscript
𝑎
𝑝
{\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
b
,
b
1
,
…
,
b
q
𝑏
subscript
𝑏
1
…
subscript
𝑏
𝑞
{\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
Identifiers
