On generalized Fibonacci and Lucas polynomials |
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Authors: | Ayse Nalli Pentti Haukkanen |
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Affiliation: | aDepartment of Mathematics, Faculty of Sciences, Selcuk University, 42075 Campus-Konya, Turkey;bDepartment of Mathematics, Statistics and Philosophy, 33014 University of Tampere , Finland |
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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 Qh(x) that generalizes the Q-matrix whose powers generate the Fibonacci numbers. |
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