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:35.8.E7 - MaRDI portal
Statements
F
2
3
(
a
1
,
a
2
,
a
3
b
1
,
b
2
;
𝐈
)
=
Γ
m
(
b
1
)
Γ
m
(
b
2
)
Γ
(
c
)
Γ
m
(
a
1
)
Γ
m
(
c
+
a
2
)
Γ
(
c
+
a
3
)
F
2
3
(
b
1
-
a
1
,
b
2
-
a
2
,
c
c
+
a
2
,
c
+
a
3
;
𝐈
)
,
Gauss-hypergeometric-of-matrix-pFq
3
2
subscript
𝑎
1
subscript
𝑎
2
subscript
𝑎
3
subscript
𝑏
1
subscript
𝑏
2
𝐈
multivariate-Euler-Gamma
𝑚
subscript
𝑏
1
multivariate-Euler-Gamma
𝑚
subscript
𝑏
2
Euler-Gamma
𝑐
multivariate-Euler-Gamma
𝑚
subscript
𝑎
1
multivariate-Euler-Gamma
𝑚
𝑐
subscript
𝑎
2
Euler-Gamma
𝑐
subscript
𝑎
3
Gauss-hypergeometric-of-matrix-pFq
3
2
subscript
𝑏
1
subscript
𝑎
1
subscript
𝑏
2
subscript
𝑎
2
𝑐
𝑐
subscript
𝑎
2
𝑐
subscript
𝑎
3
𝐈
{\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b%
_{2}};\mathbf{I}\right)=\frac{\Gamma_{m}\left(b_{1}\right)\Gamma_{m}\left(b_{2%
}\right)\Gamma\left(c\right)}{\Gamma_{m}\left(a_{1}\right)\Gamma_{m}\left(c+a_%
{2}\right)\Gamma\left(c+a_{3}\right)}\*{{}_{3}F_{2}}\left({b_{1}-a_{1},b_{2}-a%
_{2},c\atop c+a_{2},c+a_{3}};\mathbf{I}\right),}}
ℜ
(
b
1
)
subscript
𝑏
1
{\displaystyle{\displaystyle\Re(b_{1})}}
ℜ
(
b
2
)
subscript
𝑏
2
{\displaystyle{\displaystyle\Re(b_{2})}}
ℜ
(
c
)
>
1
2
(
m
-
1
)
𝑐
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(c)>\frac{1}{2}(m-1)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
q
p
(
a
1
,
…
,
a
p
;
b
1
,
…
,
b
q
;
𝐓
)
Gauss-hypergeometric-of-matrix-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝐓
{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots%
,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}
Γ
m
(
a
)
multivariate-Euler-Gamma
𝑚
𝑎
{\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
