Asymptotic behavior of varying discrete Jacobi--Sobolev orthogonal polynomials

2016/01/07 by Juan F. Mañas-Mañas, Mañas-Mañas, Juan F., Francisco Marcellán +3
Mathematics · #33C47 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C47 #msc:42C05

paper · pdf · doi:10.48550/arxiv.1601.01650

18 pages, 4 figures, 8 tables corresponding to numerical experiments. Journal of Computational and Applied Mathematics, accepted

arxiv created 2016/01/07 · arxiv updated 2016/01/08

Abstract

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.

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