Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials

Abstract

In this study we define and study the Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials. We give generating function, Binet formula, explicit formula, Q matrix, determinantal representations and partial derivation of these polynomials. By defining these Gaussian polynomials for special cases G J(n) (1) is the Gaussian Jacobsthal numbers, G j(n) (1) is the Gaussian Jacobsthal Lucas numbers defined in [2].