Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis

Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis

We study the three-term recurrence coefficients βn,γn, of polynomial sequences orthogonal with respect to a perturbed linear functional depending on a variable z. We obtain power series expansions in z, and asymptotic expansions as n →∞. We use our results to settle some conjectures proposed by Walt...

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Bibliographic Details
Main Author: Diego Dominici
Format: Article
Language:English
Published: World Scientific Publishing 2020-08-01
Series:Bulletin of Mathematical Sciences
Subjects:
toda lattice
orthogonal polynomials
recurrence coefficients
Online Access:http://www.worldscientific.com/doi/pdf/10.1142/S1664360720500034
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spelling doaj-f288a2edc8df40e99141346b32377e0d2020-11-25T03:21:28ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152020-08-011022050003-12050003-3210.1142/S166436072050003410.1142/S1664360720500034Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysisDiego Dominici0Johannes Kepler University Linz, Doktoratskolleg “Computational Mathematics”, Altenberger Straße 69, Linz 4040, AustriaWe study the three-term recurrence coefficients βn,γn, of polynomial sequences orthogonal with respect to a perturbed linear functional depending on a variable z. We obtain power series expansions in z, and asymptotic expansions as n →∞. We use our results to settle some conjectures proposed by Walter Van Assche and collaborators.http://www.worldscientific.com/doi/pdf/10.1142/S1664360720500034toda latticeorthogonal polynomialsrecurrence coefficients
collection DOAJ
language English
format Article
sources DOAJ
author Diego Dominici
spellingShingle Diego Dominici
Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
Bulletin of Mathematical Sciences
toda lattice
orthogonal polynomials
recurrence coefficients
author_facet Diego Dominici
author_sort Diego Dominici
title Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
title_short Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
title_full Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
title_fullStr Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
title_full_unstemmed Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis
title_sort recurrence coefficients of toda-type orthogonal polynomials i. asymptotic analysis
publisher World Scientific Publishing
series Bulletin of Mathematical Sciences
issn 1664-3607
1664-3615
publishDate 2020-08-01
description We study the three-term recurrence coefficients βn,γn, of polynomial sequences orthogonal with respect to a perturbed linear functional depending on a variable z. We obtain power series expansions in z, and asymptotic expansions as n →∞. We use our results to settle some conjectures proposed by Walter Van Assche and collaborators.
topic toda lattice
orthogonal polynomials
recurrence coefficients
url http://www.worldscientific.com/doi/pdf/10.1142/S1664360720500034
work_keys_str_mv AT diegodominici recurrencecoefficientsoftodatypeorthogonalpolynomialsiasymptoticanalysis
_version_ 1724614484433043456

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