On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach


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YILMAZ F., ÖZKAN M.

Axioms, vol.11, no.6, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.3390/axioms11060255
  • Journal Name: Axioms
  • Journal Indexes: Scopus
  • Keywords: Chebyshev polynomials of second kind, determinant, Horadam sequence, tridiagonal matrices
  • Ankara Haci Bayram Veli University Affiliated: No

Abstract

© 2022 by the authors. Licensee MDPI, Basel, Switzerland.In this paper, we consider an approach based on the elementary matrix theory. In other words, we take into account the generalized Gaussian Fibonacci numbers. In this context, we consider a general tridiagonal matrix family. Then, we obtain determinants of the matrix family via the Chebyshev polynomials. Moreover, we consider one type of tridiagonal matrix, whose determinants are Horadam hybrid polynomials, i.e., the most general form of hybrid numbers. Then, we obtain its determinants by means of the Chebyshev polynomials of the second kind. We provided several illustrative examples, as well.