### On Generalized Fibonacci Polynomials: Horadam Polynomials

Yüksel Soykan
Published: 9 September 2022

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

#### Scifeed alert for new publications

Never miss any articles matching your research from any publisher