Abstract
Let 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 1 1 1 0 whose powers generate the Fibonacci numbers.
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