The Bivariate Horadam Polynomials and Hybrinomials

Abstract

In this paper, we define the Horadam polynomials and hybrinomials with two variables x and y; called the bivariate Horadam polynomials and hybrinomials, respectively. Also, we obtain Binet formula, generating function and some properties for the bivariate Horadam hybrinomials. Moreover, we get Catalan, Cassini and d’Ocagne identities for these hybrinomials. Finally, the matrix representations of the bivariate Horadam hybrinomials were introduced.