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Statements
â«
đ
etr
âĄ
(
-
đđ
)
âą
|
đ
|
a
-
1
2
âą
(
m
+
1
)
âą
Z
Îș
âĄ
(
đ
)
âą
d
đ
=
Î
m
âĄ
(
a
+
Îș
)
âą
|
đ
|
-
a
âą
Z
Îș
âĄ
(
đ
-
1
)
,
subscript
đ
exponential-trace
đđ
superscript
đ
đ
1
2
đ
1
zonal-polynomial
đ
đ
đ
multivariate-Euler-Gamma
đ
đ
đ
superscript
đ
đ
zonal-polynomial
đ
superscript
đ
1
{\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}\mathrm{etr}\left(-%
\mathbf{T}\mathbf{X}\right)\,|\mathbf{X}|^{a-\frac{1}{2}(m+1)}Z_{\kappa}\left(%
\mathbf{X}\right)\mathrm{d}\mathbf{X}=\Gamma_{m}\left(a+\kappa\right)\,|%
\mathbf{T}|^{-a}Z_{\kappa}\left(\mathbf{T}^{-1}\right),}}
d
x
đ„
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
etr
âĄ
(
đ
)
exponential-trace
đ
{\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}
â«
{\displaystyle{\displaystyle\int}}
Î
m
âĄ
(
a
)
multivariate-Euler-Gamma
đ
đ
{\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}
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}}}
đ
đ
{\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}
m
đ
{\displaystyle{\displaystyle m}}
Identifiers
