  In this paper we consider sequences of polynomials orthogonal with respect to
certain discrete Laguerre-Sobolev inner product, with two perturbations
(involving derivatives) located inside the oscillatory region for the classical
Laguerre polynomials. We focus our attention on the representation of these
polynomials in terms of the classical Laguerre polynomials and deduce the
coefficients of their corresponding five-term recurrence relation, as well as
the asymptotic behavior of these coefficients when the degree of the
polynomials tends to infinity. Also, the outer relative asymptotics of
orthogonal polynomials with respect to this discrete Sobolev inner product is
analyzed.
