Connection coefficients for Laguerre--Sobolev orthogonal polynomials.
type: Item
instance of: scholarly article
title: Connection coefficients for Laguerre--Sobolev orthogonal polynomials.
zbMATH Open document ID: 1033.42027
DOI: 10.1016/S0022-247X(03)00263-4
author: Jorge Sánchez-Ruiz
author: Francisco Marcellán
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-08-25T00:00:00Z
review text: The connection problem in the framework of orthogonal polynomials is the problem of finding explicit and/or recurrence relations for the so-called connection coefficients \(c_j(n)\) of the expansion of an orthogonal family \(q_m\) in terms of another orthogonal polynomial sequence \((p_k)\) \[ q_m(x) =\sum_{j=0}^{m} c_{j}(m) p_j(x). \] In the paper the authors are interested in finding closed analytical formulas for the connection coefficients \(c_{j}(m)\) when one or both families are instances of Laguerre-Sobolev and Laguerre-Sobolev-type orthogonal polynomials. Of particular interest are the expansions of such Sobolev families in terms of the classical Laguerre polynomials as well as the corresponding inversion formulas. Finally, some open problems are posed and discussed.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1970828
zbMATH Keywords: Sobolev inner products
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: connection coefficients
reviewed by: Renato Álvarez-Nodarse
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970828