On Generalized Fibonacci Polynomials: Horadam Polynomials
Earthline Journal of Mathematical Sciences , Volume 11, pp 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: Horadam / functions / Fibonacci Polynomials / generalized Fibonacci / formulas / Lucas / give / summation
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