Summary: Let be a polynomial with real coefficients. We introduce -Fibonacci polynomials that generalize both Catalan’s Fibonacci polynomials and Byrd’s Fibonacci polynomials and also the -Fibonacci numbers, and we provide properties for these -Fibonacci polynomials. We also introduce -Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix that generalizes the -matrix whose powers generate the Fibonacci numbers.
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