# On Generalized Fibonacci Polynomials: Horadam Polynomials

• Yüksel Soykan Department of Mathematics, Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey
Keywords: Horadam polynomials, (r, s)-Fibonacci polynomials, (r, s)-Lucas polynomials, generalized Fibonacci polynomials, Fibonacci polynomials, Lucas polynomials

### 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.

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Published
2022-09-09
How to Cite
Soykan, Y. (2022). On Generalized Fibonacci Polynomials: Horadam Polynomials. Earthline Journal of Mathematical Sciences, 11(1), 23-114. https://doi.org/10.34198/ejms.11123.23114
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