Varying discrete Laguerre-Sobolev orthogonal polynomials: Asymptotic behavior and zeros

We consider a varying discrete Sobolev inner product involving the Laguerre weight. Our aim is to study the asymptotic properties of the corresponding orthogonal polynomials and of their zeros. We are interested in Mehler-Heine type formulas because they describe the asymptotic differences between these Sobolev orthogonal polynomials and the classical Laguerre polynomials. Moreover, they give us an approximation of the zeros of the Sobolev polynomials in terms of the zeros of other special functions. We generalize some results appeared very recently in the literature for both the varying and non-varying cases.The author FM is partially supported by Dirección General de Investigación, Ministerio de Economía y Competitividad Innovación of Spain, Grant MTM2012 36732 C03 01. The author JJMB is partially supported by Dirección General de Inves tigación, Ministerio de Ciencia e Innovación of Spain and European Regional Development Found, Grant MTM2011 28952 C02 01, and Junta de Andalucía, Research Group FQM 0229 (belonging to Campus of International Excellence CEI MAR), and projects P09 FQM 4643 and P11 FQM 7276

On asymptotic properties of Freud-Sobolev orthogonal polynomials

In this paper we consider a Sobolev inner product (f, g) S = fgd + # f # g # d (1) and we characterize the measures for which there exists an algebraic relation between the polynomials, orthogonal with respect to the measure and the polynomials, orthogonal with respect to (1), such that the number of involved terms does not depend on the degree of the polynomials. Thus, we reach in a natural way the measures associated with a Freud weight. In particular, we study the case d = dx supported on the full real axis and we analyze the connection between the so-called Nevai polynomials (associated with the Freud weight e -x ) and the Sobolev orthogonal polynomials Q n . Finally, we obtain some asymptotics for }