A different approach to Gauss Fibonacci polynomials

In this paper with the help of higher order Fibonacci polynomials, we introduce higher order Gauss Fibonacci polynomials that generalize the Gauss Fibonacci polynomials studied by Özkan and Taştan. We give a recurrence relation, Binet-like formula, generating and exponential generating functions, summation formula for the higher order Gauss Fibonacci polynomials. Moreover, we give two special matrices that we call $Q^{(s)}(x)$ and $P^{(s)}(x),$ respectively. From these matrices, we obtain a matrix representation and derive the Cassini's identity of higher order Gauss Fibonacci polynomials.