The generalized k-Fibonacci polynomials and generalized k-Lucas polynomials

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Tastan M., Özkan E., Shannon A. G.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.27, sa.2, ss.148-158, 2021 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 27 Sayı: 2
• Basım Tarihi: 2021
• Doi Numarası: 10.7546/nntdm.2021.27.2.148-158
• Dergi Adı: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
• Derginin Tarandığı İndeksler: Other Indexes
• Sayfa Sayıları: ss.148-158
• Anahtar Kelimeler: Generalized Fibonacci polynomials, k-Fibonacci numbers, Generalized Lucas polynomials, k-Lucas numbers, FAMILY
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Marmara Üniversitesi Adresli: Hayır

Özet

In this paper, we define new families of Generalized Fibonacci polynomials and Generalized Lucas polynomials and develop some elegant properties of these families. We also find the relationships between the family of the generalized k-Fibonacci polynomials and the known generalized Fibonacci polynomials. Furthermore, we find new generalizations of these families and the polynomials in matrix representation. Then we establish Cassini's Identities for the families and their polynomials. Finally, we suggest avenues for further research.