\[{{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=\frac{1}{\mathrm{B}_{m}\left(a%
,b-a\right)}\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I}}\operatorname{%
etr}\left(\mathbf{T}\mathbf{X}\right)\left|\mathbf{X}\right|^{a-\frac{1}{2}(m+%
1)}\left|\mathbf{I}-\mathbf{X}\right|^{b-a-\frac{1}{2}(m+1)}\,\mathrm{d}{%
\mathbf{X}},\]