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