GENERALIZED GAUSSIAN JACOBSTHAL POLYNOMIALS AND GENERALIZED GAUSSIAN JACOBSTHAL LUCAS POLYNOMIALS

Abstract

In this paper we introduce and study generalized Gaussian Jacobsthal polynomials and generalized Gaussian Jacobsthal Lucas polynomials, where $m\geq 2$. For $m=2$ these polynomials are Gaussian Jacobsthal polynomials and Gaussian Jacobsthal Lucas polynomials, respectively. We find the generating functions, explicit representations and some interesting properties for these generalized polynomials.