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Statements
F
2
3
(
a
1
,
a
2
,
a
3
b
1
,
b
2
;
𝐈
)
=
Γ
m
(
b
2
)
Γ
m
(
c
)
Γ
m
(
b
2
-
a
3
)
Γ
m
(
c
+
a
3
)
F
2
3
(
b
1
-
a
1
,
b
1
-
a
2
,
a
3
b
1
,
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
2
multivariate-Euler-Gamma
𝑚
𝑐
multivariate-Euler-Gamma
𝑚
subscript
𝑏
2
subscript
𝑎
3
multivariate-Euler-Gamma
𝑚
𝑐
subscript
𝑎
3
Gauss-hypergeometric-of-matrix-pFq
3
2
subscript
𝑏
1
subscript
𝑎
1
subscript
𝑏
1
subscript
𝑎
2
subscript
𝑎
3
subscript
𝑏
1
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_{2}\right)\Gamma_{m}\left(c%
\right)}{\Gamma_{m}\left(b_{2}-a_{3}\right)\Gamma_{m}\left(c+a_{3}\right)}\*{{%
}_{3}F_{2}}\left({b_{1}-a_{1},b_{1}-a_{2},a_{3}\atop b_{1},c+a_{3}};\mathbf{I}%
\right),}}
ℜ
(
b
2
)
,
ℜ
(
c
)
>
1
2
(
m
-
1
)
subscript
𝑏
2
𝑐
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(b_{2}),\Re(c)>\frac{1}{2}(m-1)}}
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
