  This work identifies a solvable (in the sense that spectral correlation
functions can be expressed in terms of orthogonal polynomials), rotationally
invariant random matrix ensemble with a logarithmic weakly confining potential.
The ensemble, which can be interpreted as a transformed Jacobi ensemble, is in
the thermodynamic limit characterized by a Lorentzian eigenvalue density. It is
shown that spectral correlation functions can be expressed in terms of the
nonclassical Gegenbauer polynomials $C_n^{(-1/2)}(x)$ with $n \ge 2$, which
have been proven to form a complete orthogonal set with respect to the proper
weight function. A procedure to sample matrices from the ensemble is outlined
and used to provide a numerical verification for some of the analytical
results. This ensemble is pointed out to potentially have applications in
quantum many-body physics.
