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

Carlos M. da Fonseca

doi:10.2478/ausm-2020-0019

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

Acta Universitatis Sapientiae, Mathematica

Volume 12 (2020): Issue 2 (November 2020)

By: Carlos M. da Fonseca

Open Access

|Dec 2020

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.

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2020-0019 | Journal eISSN: 2066-7752

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Language: English

Page range: 280 - 286

Submitted on: Nov 20, 2019

Published online: Dec 2, 2020

Published in print: Nov 1, 2020

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

tridiagonal matrices,

Chebyshev polynomials of second kind,

determinant,

Fibonacci numbers

MSC:

11B37,

11B39,

15A15,

15B05,

15B36,

39A10,

42C05

Related subjects:

Mathematics,

General mathematics

© 2020 Carlos M. da Fonseca, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2020): Issue 2 (November 2020)