  The paper examines rational Darboux transformations (RDTs) of the Jacobi
equation written in the canonical form, with emphasis on the Sturm-Liouville
problems (SLPs) solved under the Dirichlet boundary conditions (DBCs) at the
ends of the infinite interval [1, inf). To be able to extend the analysis to
the Darboux-Crum net of rational SL equations (SLEs) solved under the cited
DBCs in terms of multi-indexed orthogonal exceptional Romanovski-Jacobi
(XR-Jacobi) polynomials, we consider only seed functions which represent
principal Frobenius solutions (PFSs) near one of the singular endpoints. .
There are three distinct types of such solutions with no zeros inside the
selected interval: two infinite sequences formed by the PFSs near the lower
endpoint and one finite sequence formed by the PFSs near infinity. It is shown
that use of classical Jacobi polynomials as seed functions results in the
double-indexed manifold composed of orthogonal X_m-Jacobi polynomials in the
reversed argument. As a result polynomials from this manifold obey the
cross-orthogonality relation when integrated from +1 to inf. As a corollary we
assert that each X_m-Jacobi polynomial of degree m + n has exactly m
exceptional zeros between -inf and -1 as far as its indexes are restricted by
the derived constraints on indexes of XR-Jacobi polynomials.
