Asymptotic properties of Laguerre-Sobolev type orthogonal polynomials

In this contribution we consider the asymptotic behavior of sequences of monic polynomials orthogonal with respect to a Sobolev-type inner product < p, q >(S) = integral(infinity)(0) 1p(x)q(x)x(alpha)e(-x)dx + Np'(a)q' (a), alpha < -1 where N is an element of R+ , and a is an element of R-. We study the outer relative asymptotics of these polynomials with respect to the standard Laguerre polynomials. The analogue of the Mehler-Heine formula as well as a Plancherel-Rotach formula for the rescaled polynomials are given. The behavior of their zeros is also analyzed in terms of their dependence on N.