Generalizations of the Fibonacci and Lucas polynomials

Abstract

In this note we consider two sequences of polynomials, which are denoted by {Un(k),m} and {Vn(k),m}, where k, m, n are nonnegative integers, and m ? 2. These sequences represent generalizations of the well-known Fibonacci and Lucas polynomials. For example, if m = 2, then we obtain exactly the Fibonacci and Lucas polynomials. If m = 3, then polynomials Un(k),3 and Vn (k),3 were considered in papers (G. B. Djordjevic, Fibonacci Quart. 39.2(2001), and G. B. Djordjevic, Fibonacci Quart. 43.4(2005)).