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Statements
∫
𝛀
etr
(
-
𝐓𝐗
)
|
𝐗
|
γ
-
1
2
(
m
+
1
)
F
q
p
(
a
1
,
…
,
a
p
b
1
,
…
,
b
q
;
-
𝐗
)
d
𝐗
=
Γ
m
(
γ
)
|
𝐓
|
-
γ
F
q
p
+
1
(
a
1
,
…
,
a
p
,
γ
b
1
,
…
,
b
q
;
-
𝐓
-
1
)
,
subscript
𝛀
exponential-trace
𝐓𝐗
superscript
𝐗
𝛾
1
2
𝑚
1
Gauss-hypergeometric-of-matrix-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝐗
𝐗
multivariate-Euler-Gamma
𝑚
𝛾
superscript
𝐓
𝛾
Gauss-hypergeometric-of-matrix-pFq
𝑝
1
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
𝛾
subscript
𝑏
1
…
subscript
𝑏
𝑞
superscript
𝐓
1
{\displaystyle{\displaystyle{\int_{\boldsymbol{\Omega}}\mathrm{etr}\left(-%
\mathbf{T}\mathbf{X}\right)|\mathbf{X}|^{\gamma-\frac{1}{2}(m+1)}\*{{}_{p}F_{q%
}}\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};-\mathbf{X}\right)\mathrm{d%
}\mathbf{X}}=\Gamma_{m}\left(\gamma\right)|\mathbf{T}|^{-\gamma}{{}_{p+1}F_{q}%
}\left({a_{1},\dots,a_{p},\gamma\atop b_{1},\dots,b_{q}};-\mathbf{T}^{-1}%
\right),}}
ℜ
(
γ
)
>
1
2
(
m
-
1
)
𝛾
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(\gamma)>\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}}}
etr
(
𝐗
)
exponential-trace
𝐗
{\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}
∫
{\displaystyle{\displaystyle\int}}
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}}
𝐓
𝐓
{\displaystyle{\displaystyle\mathbf{T}}}
𝐗
𝐗
{\displaystyle{\displaystyle\mathbf{X}}}
𝛀
𝛀
{\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}
b
𝑏
{\displaystyle{\displaystyle b}}
p
𝑝
{\displaystyle{\displaystyle p}}
q
𝑞
{\displaystyle{\displaystyle q}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
