\[\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I}}\left|\mathbf{X}\right|^{a%
-\frac{1}{2}(m+1)}\*\left|\mathbf{I}-\mathbf{X}\right|^{b-\frac{1}{2}(m+1)}Z_{%
\kappa}\left(\mathbf{T}\mathbf{X}\right)\,\mathrm{d}{\mathbf{X}}=\frac{{\left[%
a\right]_{\kappa}}}{{\left[a+b\right]_{\kappa}}}\mathrm{B}_{m}\left(a,b\right)%
Z_{\kappa}\left(\mathbf{T}\right).\]