Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:35.6.E5 - MaRDI portal
Statements
∫
𝛀
etr
(
-
𝐓𝐗
)
|
𝐗
|
b
-
1
2
(
m
+
1
)
F
1
1
(
a
b
;
𝐒𝐗
)
d
𝐗
=
Γ
m
(
b
)
|
𝐈
-
𝐒𝐓
-
1
|
-
a
|
𝐓
|
-
b
,
subscript
𝛀
exponential-trace
𝐓𝐗
superscript
𝐗
𝑏
1
2
𝑚
1
Gauss-hypergeometric-of-matrix-pFq
1
1
𝑎
𝑏
𝐒𝐗
𝐗
multivariate-Euler-Gamma
𝑚
𝑏
superscript
𝐈
superscript
𝐒𝐓
1
𝑎
superscript
𝐓
𝑏
{\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}\mathrm{etr}\left(-%
\mathbf{T}\mathbf{X}\right)|\mathbf{X}|^{b-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left%
({a\atop b};\mathbf{S}\mathbf{X}\right)\mathrm{d}\mathbf{X}=\Gamma_{m}\left(b%
\right)|\mathbf{I}-\mathbf{S}\mathbf{T}^{-1}|^{-a}|\mathbf{T}|^{-b},}}
ℜ
(
b
)
>
1
2
(
m
-
1
)
𝑏
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(b)>\frac{1}{2}(m-1)}}
𝐓
>
𝐒
𝐓
𝐒
{\displaystyle{\displaystyle\mathbf{T}>\mathbf{S}}}
ℜ
(
b
)
>
1
2
(
m
-
1
)
𝑏
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(b)>\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}}
𝐒
𝐒
{\displaystyle{\displaystyle\mathbf{S}}}
𝐓
𝐓
{\displaystyle{\displaystyle\mathbf{T}}}
𝐗
𝐗
{\displaystyle{\displaystyle\mathbf{X}}}
𝛀
𝛀
{\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}
b
𝑏
{\displaystyle{\displaystyle b}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
