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


YILMAZ F., ÖZKAN M.

AXIOMS, vol.11, no.6, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.3390/axioms11060255
  • Journal Name: AXIOMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Horadam sequence, Chebyshev polynomials of second kind, determinant, tridiagonal matrices, PELL, JACOBSTHAL, SEQUENCE
  • Gazi University Affiliated: Yes

Abstract

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.