A DIFFERENT APPROACH TO GAUSS FIBONACCI POLYNOMIALS
Can Kizilates
article (Uluslararası, Hakemli) | Yazar(lar): Can Kizilates | Yıl: 2024 | Dergi/Kurum: CONTRIBUTIONS TO DISCRETE MATHEMATICS | İndeks: WOS.SCI | Anahtar Kelimeler: Gauss Fibonacci polynomials, Higher order Gauss Fibonacci polynomials, Recurrence relation, Generating functions, Summation formula, Matrix representation —
In this paper with the help of higher order Fibonacci polynomials, we introduce higher order Gauss Fibonacci polynomials that generalize the Gauss Fibonacci polynomials studied by Ozkan and Tastan [14]. We give a recurrence relation, Binet-like formula, generating and exponential generating functions, summation formula for the higher order Gauss Fibonacci polynomials. Moreover, we give two special matrices that we call Q((s))(x) and P-(s)(x), respectively. From these matrices, we obtain a matrix representation and derive the Cassini's identity of higher order Gauss Fibonacci polynomials.