On the constant coefficients of a certain recurrence relation: A simple proof

In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.

Bibliographic Details
Main Authors:	Milica Anđelić, Carlos M. da Fonseca
Format:	Article
Language:	English
Published:	Elsevier 2021-08-01
Series:	Heliyon
Subjects:	Recurrence relation Determinant Tridiagonal k-Toeplitz matrices Chebyshev polynomials of second kind
Online Access:	http://www.sciencedirect.com/science/article/pii/S2405844021018673

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spelling	doaj-0e7c7b30675c4f92b2c87fb5d5d7a5952021-09-01T12:17:21ZengElsevierHeliyon2405-84402021-08-0178e07764On the constant coefficients of a certain recurrence relation: A simple proofMilica Anđelić0Carlos M. da Fonseca1Department of Mathematics, Kuwait University, Safat 13060, KuwaitKuwait College of Science and Technology, Doha District, Safat 13133, Kuwait; Chair of Computational Mathematics, University of Deusto, 48007 Bilbao, Basque Country, Spain; Corresponding author at: Kuwait College of Science and Technology, Doha District, Safat 13133, Kuwait.In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.http://www.sciencedirect.com/science/article/pii/S2405844021018673Recurrence relationDeterminantTridiagonal k-Toeplitz matricesChebyshev polynomials of second kind
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Milica Anđelić Carlos M. da Fonseca
spellingShingle	Milica Anđelić Carlos M. da Fonseca On the constant coefficients of a certain recurrence relation: A simple proof Heliyon Recurrence relation Determinant Tridiagonal k-Toeplitz matrices Chebyshev polynomials of second kind
author_facet	Milica Anđelić Carlos M. da Fonseca
author_sort	Milica Anđelić
title	On the constant coefficients of a certain recurrence relation: A simple proof
title_short	On the constant coefficients of a certain recurrence relation: A simple proof
title_full	On the constant coefficients of a certain recurrence relation: A simple proof
title_fullStr	On the constant coefficients of a certain recurrence relation: A simple proof
title_full_unstemmed	On the constant coefficients of a certain recurrence relation: A simple proof
title_sort	on the constant coefficients of a certain recurrence relation: a simple proof
publisher	Elsevier
series	Heliyon
issn	2405-8440
publishDate	2021-08-01
description	In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.
topic	Recurrence relation Determinant Tridiagonal k-Toeplitz matrices Chebyshev polynomials of second kind
url	http://www.sciencedirect.com/science/article/pii/S2405844021018673
work_keys_str_mv	AT milicaanđelic ontheconstantcoefficientsofacertainrecurrencerelationasimpleproof AT carlosmdafonseca ontheconstantcoefficientsofacertainrecurrencerelationasimpleproof
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On the constant coefficients of a certain recurrence relation: A simple proof

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