On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers-Reference-Cited by-同舟云学术

On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers

Published:2020-11-01 Issue:2 Volume:12 Page:280-286
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

da Fonseca Carlos M.¹

Affiliation:

1. Kuwait College of Science and Technology , Doha District, Block 4, P.O. Box 27235, Safat 13133 , Kuwait

Abstract

Abstract In this note, we recall several connections between the determinant of some tridiagonal matrices and the orthogonal polynomials allowing the relation between Chebyshev polynomials of second kind and Fibonacci numbers. With basic transformations, we are able to recover some recent results on this matter, bringing them into one place.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/ausm-2020-0019

Reference21 articles.

1. [1] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth edition, Dover Publications, Inc., New York, 1970.

2. [2] M. Andelić, Z. Du, C. M. da Fonseca, E. Kılıç, A matrix approach to some second-order difference equations with sign-alternating coefficients, J. Difference Equ. Appl., 26 (2020), 149–162.10.1080/10236198.2019.1709180

3. [3] M. Anđelić, C. M. da Fonseca, A determinantal formula for generalized Fibonacci numbers, Matematiche (Catania), 74 (2019), 363–367.

4. [4] G. B. Arfken, H. J. Weber, F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, Academic Press, Orlando, 1985.

5. [5] R. G. Buschman, Fibonacci numbers, Chebyshev polynomials generalizations and difference equations, Fibonacci Quart. 1 (1963), 1–8, 19.

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