Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials and their properties

Abstract

In this paper, the Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials are defined. Then Binet formula and generating functions of these numbers are given. Also, some summation identities for Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials are obtained by using the recurrence relation satisfied by them. Then, some linear and quadratic relations are given between Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials.