Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme
type: Item
instance of: scholarly article
title: Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme
zbMATH Open document ID: 1204.33009
DOI: 10.1155/2009/268134
author: Mario Bruschi
author: Francesco Calogero
author: R. Droghei
published in: Advances in Mathematical Physics
publication date: 2010-11-16T00:00:00Z
full work available at URL: https://eudml.org/doc/227628
review text: Summary: In this paper, we apply to (almost) all the ``named'' polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros-generally given by simple expressions in terms of integers (diophantine relations). The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold. Most of these results are not (yet) reported in the standard compilations.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 5816335
Wikidata QID: Q58646961
MaRDI profile type: Publication
OpenAlex ID: W2025946518
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description: scientific article; zbMATH DE number 5816335