\[\int_{\boldsymbol{\Omega}}\operatorname{etr}\left(-\mathbf{T}\mathbf{X}\right)%
\,\left|\mathbf{X}\right|^{a-\frac{1}{2}(m+1)}Z_{\kappa}\left(\mathbf{X}\right%
)\,\mathrm{d}{\mathbf{X}}=\Gamma_{m}\left(a+\kappa\right)\,\left|\mathbf{T}%
\right|^{-a}Z_{\kappa}\left(\mathbf{T}^{-1}\right),\]