\[{{}_{2}F_{1}}\left({a,b\atop c};\mathbf{T}\right)=\left|\mathbf{I}-\mathbf{T}%
\right|^{c-a-b}{{}_{2}F_{1}}\left({c-a,c-b\atop c};\mathbf{T}\right)=\left|%
\mathbf{I}-\mathbf{T}\right|^{-a}{{}_{2}F_{1}}\left({a,c-b\atop c};-\mathbf{T}%
(\mathbf{I}-\mathbf{T})^{-1}\right)=\left|\mathbf{I}-\mathbf{T}\right|^{-b}{{}%
_{2}F_{1}}\left({c-a,b\atop c};-\mathbf{T}(\mathbf{I}-\mathbf{T})^{-1}\right).\]