d-Gaussian Fibonacci, d-Gaussian Lucas Polynomials, and their Matrix Representations

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Ukrainian Mathematical Journal, vol.75, no.4, pp.562-585, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 75 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1007/s11253-023-02217-3
  • Journal Name: Ukrainian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.562-585
  • Erzincan Binali Yildirim University Affiliated: Yes


We define d-Gaussian Fibonacci polynomials and d-Gaussian Lucas polynomials and present matrix representations of these polynomials. By using the Riordan method, we obtain the factorizations of the Pascal matrix, including polynomials. In addition, we define the infinite d-Gaussian Fibonacci polynomial matrix and the d-Gaussian Lucas polynomial matrix and present their inverses.