k-Fibonacci Polynomials in The Family of Fibonacci Numbers

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Özkan E., Taştan M.

Research & Reviews: Discrete Mathematical Structures, cilt.6, sa.3, ss.19-22, 2019 (Hakemli Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 3
  • Basım Tarihi: 2019
  • Dergi Adı: Research & Reviews: Discrete Mathematical Structures
  • Derginin Tarandığı İndeksler: Other Indexes
  • Sayfa Sayıları: ss.19-22
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In this study, we define k-Fibonacci Polynomials by using terms of a new family of Fibonacci numbers given by Mikkawy and Sogabe. We compare the polynomials with known Fibonacci polynomial. Furthermore, we show the relationship between Pascal’s triangle and the coefficient of the k-Fibonacci polynomials. We give some important properties of the polynomial.

2010 Mathematics Subject Classification: 11B39.

Keywords: Fibonacci Numbers, Fibonacci Polynomials, Pascal’s triangle, k-Fibonacci polynomials, The derivative of the k-Fibonacci polynomial