Asymptotic behavior of varying discrete Jacobi-Sobolev orthogonal polynomials

In this contribution we deal with a varying discrete Sobolev inner product involving the Jacobi weight. Our aim is to study the asymptotic properties of the corresponding orthogonal polynomials and the behavior of their zeros. We are interested in Mehler-Heine type formulae because they describe the essential differences from the point of view of the asymptotic behavior between these Sobolev orthogonal polynomials and the Jacobi ones. Moreover, this asymptotic behavior provides an approximation of the zeros of the Sobolev polynomials in terms of the zeros of other well-known special functions. We generalize some results appeared in the literature very recently. (C) 2016 Elsevier B.V. All rights reserved.The authors JFMM and JJMB are partially supported by Research Group FQM-0229 (belonging to Campus of International Excellence CEIMAR). The author JFMM is funded by a grant of Plan Propio de la Universidad de Almería. 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 Investigación, Ministerio de Ciencia e Innovación of Spain and European Regional Development Found, grants MTM2011-28952-C02-01 and MTM2014-53963-P, and Junta de Andalucía (excellence grant P11-FQM-7276)