Gaussian number sequences and their polynomials

In this thesis, new families of Gaussian number sequences are defined. Gauss Fibonacci and Gauss Lucas polynomials have been defined and their relations with known families have been investigated. The relationship between Gauss k-Fibonacci polynomials and known Gaussian Fibonacci polynomials and Gauss k-Lucas numbers and polynomials with known Lucas numbers and polynomials are given. The relationship between the Gauss k-Jacobsthal numbers and the known Jacobsthal numbers and the Gauss k- Jacobsthal-Lucas numbers and the known Jacobsthal-Lucas numbers are given. In addition, this Gauss k-Jacobsthal number sequence and the polynomials of Gauss k-Jacobsthal-Lucas number sequences are defined. Some properties of these polynomials have been obtained. The relationship between the Gauss k-Jacobsthal polynomials and the known Jacobsthal polynomials and the Gauss k-Jacobsthal-Lucas polynomials and the known Jacobsthal-Lucas polynomials are given. Finally, matrix representations of the new family and its polynomials are found.