On Gaussian Family of Generalized Fibonacci Polynomials

In this paper, we define Gaussian generalized Fibonacci polynomials as a new member of the family of Gaussian polynomials. We examine in detail the fundamental algebraic and structural properties of these polynomials, which are defined using matrix properties, and present the Binet-type formula and recurrence relations. Furthermore, we give some identities involving these polynomials. Finally, we derive generating and exponential generating functions of these polynomials.