Asymptotic behavior of varying discrete Jacobi-Sobolev orthogonal polynomials Articles uri icon

publication date

  • July 2016

start page

  • 341

end page

  • 353

volume

  • 300

international standard serial number (ISSN)

  • 0377-0427

electronic international standard serial number (EISSN)

  • 1879-1778

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. (C) 2016 Elsevier B.V. All rights reserved.

keywords

  • sobolev orthogonal polynomials; jacobi polynomials; mehler-heine formulae; asymptotics; zeros