\[{\int_{\boldsymbol{\Omega}}\operatorname{etr}\left(-\mathbf{T}\mathbf{X}\right%
)\left|\mathbf{X}\right|^{\gamma-\frac{1}{2}(m+1)}\*{{}_{p}F_{q}}\left({a_{1},%
\dots,a_{p}\atop b_{1},\dots,b_{q}};-\mathbf{X}\right)\,\mathrm{d}{\mathbf{X}}%
}=\Gamma_{m}\left(\gamma\right)\left|\mathbf{T}\right|^{-\gamma}{{}_{p+1}F_{q}%
}\left({a_{1},\dots,a_{p},\gamma\atop b_{1},\dots,b_{q}};-\mathbf{T}^{-1}%
\right),\]