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Statements
F
1
1
(
a
b
;
𝐓
)
=
1
B
m
(
a
,
b
-
a
)
∫
𝟎
<
𝐗
<
𝐈
etr
(
𝐓𝐗
)
|
𝐗
|
a
-
1
2
(
m
+
1
)
|
𝐈
-
𝐗
|
b
-
a
-
1
2
(
m
+
1
)
d
𝐗
,
Gauss-hypergeometric-of-matrix-pFq
1
1
𝑎
𝑏
𝐓
1
multivariate-Euler-Beta
𝑚
𝑎
𝑏
𝑎
subscript
0
𝐗
𝐈
exponential-trace
𝐓𝐗
superscript
𝐗
𝑎
1
2
𝑚
1
superscript
𝐈
𝐗
𝑏
𝑎
1
2
𝑚
1
𝐗
{\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=%
\frac{1}{\mathrm{B}_{m}\left(a,b-a\right)}\int\limits_{\boldsymbol{{0}}<%
\mathbf{X}<\mathbf{I}}\mathrm{etr}\left(\mathbf{T}\mathbf{X}\right)|\mathbf{X}%
|^{a-\frac{1}{2}(m+1)}|\mathbf{I}-\mathbf{X}|^{b-a-\frac{1}{2}(m+1)}\mathrm{d}%
\mathbf{X},}}
ℜ
(
a
)
,
ℜ
(
b
-
a
)
>
1
2
(
m
-
1
)
𝑎
𝑏
𝑎
1
2
𝑚
1
{\displaystyle{\displaystyle\Re(a),\Re(b-a)>\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}}
B
m
(
a
,
b
)
multivariate-Euler-Beta
𝑚
𝑎
𝑏
{\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right%
)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
a
𝑎
{\displaystyle{\displaystyle a}}
𝐓
𝐓
{\displaystyle{\displaystyle\mathbf{T}}}
𝐗
𝐗
{\displaystyle{\displaystyle\mathbf{X}}}
b
𝑏
{\displaystyle{\displaystyle b}}
m
𝑚
{\displaystyle{\displaystyle m}}
Identifiers
