2-Fibonacci polynomials in the family of Fibonacci numbers


ÖZKAN E. , Taştan M., Aydogdu A.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.24, ss.47-55, 2018 (ESCI İndekslerine Giren Dergi)

  • Cilt numarası: 24 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.7546/nntdm.2018.24.3.47-55
  • Dergi Adı: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
  • Sayfa Sayısı: ss.47-55

Özet

In the present study, we define new 2-Fibonacci polynomials by using terms of a new family of Fibonacci numbers given in [4]. We show that there is a relationship between the coefficient of the 2-Fibonacci polynomials and Pascal's triangle. We give some identities of the 2-Fibonacci polynomials. Afterwards, we compare the polynomials with known Fibonacci polynomials. We also express 2-Fibonacci polynomials by the Fibonacci polynomials. Furthermore, we prove some theorems related to the polynomials. Also, we introduce the derivative of the 2-Fibonacci polynomials.