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Statements
â«
đ
<
đ
<
đ
|
đ
|
a
-
1
2
âą
(
m
+
1
)
âą
|
đ
-
đ
|
b
-
1
2
âą
(
m
+
1
)
âą
Z
Îș
âĄ
(
đđ
)
âą
d
đ
=
[
a
]
Îș
[
a
+
b
]
Îș
âą
B
m
âĄ
(
a
,
b
)
âą
Z
Îș
âĄ
(
đ
)
.
subscript
0
đ
đ
superscript
đ
đ
1
2
đ
1
superscript
đ
đ
đ
1
2
đ
1
zonal-polynomial
đ
đđ
đ
shifted-factorial
đ
đ
shifted-factorial
đ
đ
đ
multivariate-Euler-Beta
đ
đ
đ
zonal-polynomial
đ
đ
{\displaystyle{\displaystyle\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I%
}}|\mathbf{X}|^{a-\frac{1}{2}(m+1)}\*|\mathbf{I}-\mathbf{X}|^{b-\frac{1}{2}(m+%
1)}Z_{\kappa}\left(\mathbf{T}\mathbf{X}\right)\mathrm{d}\mathbf{X}=\frac{{%
\left[a\right]_{\kappa}}}{{\left[a+b\right]_{\kappa}}}\mathrm{B}_{m}\left(a,b%
\right)Z_{\kappa}\left(\mathbf{T}\right).}}
d
x
đ„
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
â«
{\displaystyle{\displaystyle\int}}
B
m
âĄ
(
a
,
b
)
multivariate-Euler-Beta
đ
đ
đ
{\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right%
)}}
[
a
]
Îș
shifted-factorial
đ
đ
{\displaystyle{\displaystyle{\left[\NVar{a}\right]_{\NVar{\kappa}}}}}
Z
Îș
âĄ
(
đ
)
zonal-polynomial
đ
đ
{\displaystyle{\displaystyle Z_{\NVar{\kappa}}\left(\NVar{\mathbf{T}}\right)}}
a
đ
{\displaystyle{\displaystyle a}}
đ
đ
{\displaystyle{\displaystyle\mathbf{T}}}
đ
đ
{\displaystyle{\displaystyle\mathbf{X}}}
b
đ
{\displaystyle{\displaystyle b}}
m
đ
{\displaystyle{\displaystyle m}}
Identifiers
