On generalized Fibonacci and Lucas polynomials

Ayse Nalli and Pentti Haukkanen

Chaos, Solitons & Fractals, 2009, vol. 42, issue 5, 3179-3186

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 1110 whose powers generate the Fibonacci numbers.

Date: 2009
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:5:p:3179-3186

DOI: 10.1016/j.chaos.2009.04.048

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