The ``classical'' Laurent biorthogonal polynomials
type: Item
instance of: scholarly article
title: The ``classical'' Laurent biorthogonal polynomials
zbMATH Open document ID: 0932.33006
DOI: 10.1016/S0377-0427(98)00118-6
author: Alexei Zhedanov
published in: Journal of Computational and Applied Mathematics
publication date: 2000-03-21T00:00:00Z
review text: In this paper an analogue of the Hahn theorem for Laurent biorthogonal polynomials (LBP) \(P_n(z)\) is studied. Necessary and sufficient conditions for derivatives \(\widetilde P_n(z)= (n+1)^{-1} P_{n+1}'(z)\) are also obtained. These conditions are derived as a linear second-order difference equation for the moments. Some special examples of such LBP which are different from the well known classical LBP are considered. Lastly the theory of spectral transformations of these polynomials is developed which is crucial in the study of LBP belonging to the Hahn class.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1326556
zbMATH Keywords: Laurent biorthogonal polynomials
zbMATH Keywords: spectral transformations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326556