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

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
Description
Summary: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.
ISSN:2405-8440

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