Nalli, AyseHaukkanen, Pentti2020-03-262020-03-2620090960-07791873-2887https://dx.doi.org/10.1016/j.chaos.2009.04.048https://hdl.handle.net/20.500.12395/23716Let h(x) be a polynomial with real coefficients. We introduce h(x)-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these h(x)-Fibonacci polynomials. We also introduce h(x)-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q(h)(x) that generalizes the Q-matrix [GRAPHICS] whose powers generate the Fibonacci numbers. (C) 2009 Elsevier Ltd. All rights reserved.en10.1016/j.chaos.2009.04.048info:eu-repo/semantics/closedAccessArticle42531793186Q1WOS:000269425200073Q1