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

YILMAZ F., ÖZKAN M.

AXIOMS, cilt.11, sa.6, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3390/axioms11060255
  • Dergi Adı: AXIOMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Horadam sequence, Chebyshev polynomials of second kind, determinant, tridiagonal matrices, PELL, JACOBSTHAL, SEQUENCE
  • Gazi Üniversitesi Adresli: Evet

Özet

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.