On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications

Özkan E., Tastan M.

COMMUNICATIONS IN ALGEBRA, cilt.48, sa.3, ss.952-960, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1080/00927872.2019.1670193
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.952-960
  • Anahtar Kelimeler: Fibonacci polynomials, Gauss Fibonacci numbers, Gauss Lucas numbers, Lucas polynomials, NUMBERS, FAMILY
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

We define the Gauss Fibonacci polynomials. Then we give a formula for the Gauss Fibonacci polynomials by using the Fibonacci polynomials. The Gauss Lucas polynomials are described and the relation with Lucas polynomials are explained. We show that there is a relation between the Gauss Fibonacci polynomials and the Fibonacci polynomials. The Gauss Lucas polynomials are also given by using the Gauss Fibonacci polynomials. Some theorems like Cassini's theorem are proved for the polynomials. Their Binet's formulas are obtained. We also define the matrices of the Gauss Fibonacci polynomials and the Gauss Lucas polynomials. We examine properties of the matrices.