On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Abstract

In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(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.

Keywords

• jacobsthal polynomials
• lucas polynomials
• generating function
• generating matrix
• catalan's identity
• d'ocagne's identity
• primary 11b83
• 11b37
• secondary 11b39
• 11c20
• 15b36