On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, J_h,n and j_h,n, respectively, that consist on an extension of Jacobsthal's polynomials J_n(𝑥) and Jacobsthal-Lucas polynomials j_n(𝑥). We provide their properties and a generalization of the usual identities. We also present, for each one of these generalized polynomials, their ordinary generating functions and matrices. In the last part of the paper, we present some special kind of tridiagonal matrices whose entries are elements of these generalized polynomials.