On Generalized Fibonacci Polynomials: Horadam Polynomials
Open Access
- 9 September 2022
- journal article
- Published by Earthline Publishers in Earthline Journal of Mathematical Sciences
- Vol. 11 (1), 23-114
- https://doi.org/10.34198/ejms.11123.23114
Abstract
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.Keywords
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