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Statements
∫
𝟎
<
𝐗
<
𝐈
|
𝐗
|
a
1
-
1
2
(
m
+
1
)
|
𝐈
-
𝐗
|
b
1
-
a
1
-
1
2
(
m
+
1
)
F
q
p
(
a
2
,
…
,
a
p
+
1
b
2
,
…
,
b
q
+
1
;
𝐓𝐗
)
d
𝐗
=
1
B
m
(
b
1
-
a
1
,
a
1
)
F
q
+
1
p
+
1
(
a
1
,
…
,
a
p
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1
b
1
,
…
,
b
q
+
1
;
𝐓
)
,
subscript
0
𝐗
𝐈
superscript
𝐗
subscript
𝑎
1
1
2
𝑚
1
superscript
𝐈
𝐗
subscript
𝑏
1
subscript
𝑎
1
1
2
𝑚
1
Gauss-hypergeometric-of-matrix-pFq
𝑝
𝑞
subscript
𝑎
2
…
subscript
𝑎
𝑝
1
subscript
𝑏
2
…
subscript
𝑏
𝑞
1
𝐓𝐗
𝐗
1
multivariate-Euler-Beta
𝑚
subscript
𝑏
1
subscript
𝑎
1
subscript
𝑎
1
Gauss-hypergeometric-of-matrix-pFq
𝑝
1
𝑞
1
subscript
𝑎
1
…
subscript
𝑎
𝑝
1
subscript
𝑏
1
…
subscript
𝑏
𝑞
1
𝐓
{\displaystyle{\displaystyle\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I%
}}|\mathbf{X}|^{a_{1}-\frac{1}{2}(m+1)}{|\mathbf{I}-\mathbf{X}|}^{b_{1}-a_{1}-%
\frac{1}{2}(m+1)}\*{{}_{p}F_{q}}\left({a_{2},\dots,a_{p+1}\atop b_{2},\dots,b_%
{q+1}};\mathbf{T}\mathbf{X}\right)\mathrm{d}\mathbf{X}=\frac{1}{\mathrm{B}_{m}%
\left(b_{1}-a_{1},a_{1}\right)}{{}_{p+1}F_{q+1}}\left({a_{1},\dots,a_{p+1}%
\atop b_{1},\dots,b_{q+1}};\mathbf{T}\right),}}
ℜ
(
b
1
-
a
1
)
,
ℜ
(
a
1
)
>
1
2
(
m
-
1
)
subscript
𝑏
1
subscript
𝑎
1
subscript
𝑎
1
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(b_{1}-a_{1}),\Re(a_{1})>\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)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
B
m
(
a
,
b
)
multivariate-Euler-Beta
𝑚
𝑎
𝑏
{\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right%
)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
a
𝑎
{\displaystyle{\displaystyle a}}
𝐓
𝐓
{\displaystyle{\displaystyle\mathbf{T}}}
𝐗
𝐗
{\displaystyle{\displaystyle\mathbf{X}}}
b
𝑏
{\displaystyle{\displaystyle b}}
p
𝑝
{\displaystyle{\displaystyle p}}
q
𝑞
{\displaystyle{\displaystyle q}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
