On generalized Fibonacci and Lucas hybrid polynomials

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Ait-Amrane N. R., Belbachir H., TAN E.

TURKISH JOURNAL OF MATHEMATICS, cilt.46, sa.6, ss.2069-2077, 2022 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.55730/1300-0098.3254
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2069-2077
  • Anahtar Kelimeler: r-Fibonacci polynomial, r-Lucas polynomial, hybrid number
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a new generalization of Fibonacci and Lucas hybrid polynomials. We investigate some basic properties of these polynomials such as recurrence relations, the generating functions, the Binet formulas, summation formulas, and a matrix representation. We derive generalized Cassini???s identity and generalized Honsberger formula for generalized Fibonacci hybrid polynomials by using their matrix representation.