A class of nonsymmetric orthogonal polynomials
type: Item
instance of: scholarly article
title: A class of nonsymmetric orthogonal polynomials
zbMATH Open document ID: 0622.33008
DOI: 10.1016/0022-247X(87)90092-8
author: Laura M. Chihara
author: Theodore S. Chihara
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(\{P_ n(x)\}\) be a sequence of polynomials orthogonal with respect to a positive measure on [0,\(\infty)\), and let \(\{K_ n(x)\}\) denote the corresponding sequence of kernel polynomials with k-parameter 0. The authors study the sequence of polynomials \(\{R_ n(x)\}\) defined by \[ R_{2n}(x) = P_ n(x^ 2)\quad +\quad \vartheta_{2n}xK_{n-1}(x^ 2), \] \[ R_{2n+1}(x) = xK_ n(x^ 2)\quad +\quad \vartheta_{2n+1}P_ n(x^ 2) \] for some sequence \(\{\vartheta_ n\}\). A necessary and sufficient condition on \(\{\vartheta_ n\}\) is determined for \(\{R_ n(x)\}\) to be orthogonal with respect to a positive measure, and this measure is then expressed in terms of the measure with respect to which \(\{P_ n(x)\}\) is orthogonal. The paper concludes with a number of exmples of orthogonal polynomial sequences of this type.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4008824
zbMATH Keywords: kernel polynomials
reviewed by: Erik A. van Doorn
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4008824