On Generalized Fibonacci Polynomials: Horadam Polynomials Article Swipe

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Fibonacci polynomials Fibonacci number Mathematics Lucas number Pisano period Classical orthogonal polynomials Wilson polynomials Difference polynomials Orthogonal polynomials Combinatorics Recurrence relation Discrete orthogonal polynomials Polynomial Lucas sequence Discrete mathematics Pure mathematics Algebra over a field Mathematical analysis

Yüksel Soykan ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.34198/ejms.11123.23114 · OA: W4296231672

In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and we deal with, in detail, two special cases which we call them $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomials. We present Binet's formulas, generating functions, Simson's formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices associated with these sequences. Finally, we present several expressions and combinatorial results of the generalized Fibonacci polynomials.