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Statements
∫
𝛀
|
𝐓
|
c
-
1
2
(
m
+
1
)
Ψ
(
a
;
b
;
𝐓
)
d
𝐓
=
Γ
m
(
c
)
Γ
m
(
a
-
c
)
Γ
m
(
c
-
b
+
1
2
(
m
+
1
)
)
Γ
m
(
a
)
Γ
m
(
a
-
b
+
1
2
(
m
+
1
)
)
,
subscript
𝛀
superscript
𝐓
𝑐
1
2
𝑚
1
confluent-hypergeometric-of-matrix-Psi
𝑎
𝑏
𝐓
𝐓
multivariate-Euler-Gamma
𝑚
𝑐
multivariate-Euler-Gamma
𝑚
𝑎
𝑐
multivariate-Euler-Gamma
𝑚
𝑐
𝑏
1
2
𝑚
1
multivariate-Euler-Gamma
𝑚
𝑎
multivariate-Euler-Gamma
𝑚
𝑎
𝑏
1
2
𝑚
1
{\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}|\mathbf{T}|^{c-\frac{1}%
{2}(m+1)}\Psi\left(a;b;\mathbf{T}\right)\mathrm{d}\mathbf{T}=\frac{\Gamma_{m}%
\left(c\right)\Gamma_{m}\left(a-c\right)\Gamma_{m}\left(c-b+\frac{1}{2}(m+1)%
\right)}{\Gamma_{m}\left(a\right)\Gamma_{m}\left(a-b+\frac{1}{2}(m+1)\right)},}}
ℜ
(
a
)
>
ℜ
(
c
)
+
1
2
(
m
-
1
)
>
m
-
1
𝑎
𝑐
1
2
𝑚
1
𝑚
1
{\displaystyle{\displaystyle\Re(a)>\Re(c)+\frac{1}{2}(m-1)>m-1}}
ℜ
(
c
-
b
)
>
-
1
𝑐
𝑏
1
{\displaystyle{\displaystyle\Re(c-b)>-1}}
Ψ
(
a
;
b
;
𝐓
)
confluent-hypergeometric-of-matrix-Psi
𝑎
𝑏
𝐓
{\displaystyle{\displaystyle\Psi\left(\NVar{a};\NVar{b};\NVar{\mathbf{T}}%
\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\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}}}
𝛀
𝛀
{\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
