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

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ÖZKAN E., UYSAL M.

Ukrainian Mathematical Journal, cilt.75, sa.4, ss.562-585, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s11253-023-02217-3
  • Dergi Adı: Ukrainian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.562-585
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

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.