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


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Taştan M., Özkan E. , Anthony G. Shannon A. G.

Notes on Number Theory and Discrete Mathematics, cilt.27, sa.2, ss.148-158, 2021 (ESCI İndekslerine Giren Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Konu: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.7546/nntdm.2021.27.2.148-158
  • Dergi Adı: Notes on Number Theory and Discrete Mathematics
  • Sayfa Sayıları: ss.148-158

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.