On orthogonal polynomials with respect to the form \(-(x-c)S'\)
type: Item
instance of: scholarly article
title: On orthogonal polynomials with respect to the form \(-(x-c)S'\)
zbMATH Open document ID: 1121.33012
author: J. Alaya
author: Ridha Sfaxi
published in: Periodica Mathematica Hungarica
publication date: 2007-01-08T00:00:00Z
review text: Let be \(S\) the classical Bessel or Jacobi linear functional and let \(u\) be the functional defined by \(u=-(x-c)S'\), which is, in general non regular. In this paper the authors establish necessary and sufficient conditions for the functional \(u\) to be regular. In fact, they proved in section 5 that under certain conditions (when \(u\) is regular), \(u\) is a semiclassical of class 1 and the corresponding orthogonal polynomial sequence satisfies certain algebraic relations (recurrence relations and structure relations) that characterize it. Finally, a concrete example of Jacobi type is worked out in details.
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 5082320
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: classical polynomials
zbMATH Keywords: semi-classical forms
zbMATH Keywords: finite-type relations
zbMATH Keywords: coherent pairs
zbMATH Keywords: diagonal sequences
reviewed by: Renato Álvarez-Nodarse
MaRDI profile type: Publication
full work available at URL: s10998-006-0006-3
OpenAlex ID: W2045829216
DOI: 10.1007/S10998-006-0006-3
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description: scientific article; zbMATH DE number 5082320