On a new family of gauss k-Lucas numbers and their polynomials

In this paper, we define a new family of Gauss k-Lucas numbers. We give the relationships between the family of the Gauss k-Lucas numbers and the known Gauss Lucas numbers. We also define the generalized polynomials for these numbers. We obtain some interesting properties of the polynomials. We also give the relationships between the generalized Gauss k-Lucas polynomials and the known Gauss Lucas polynomials. Furthermore, we find new generalizations of these families and the polynomials in matrix representation. Then we prove Cassini's identities for the families and their polynomials. © 2021 World Scientific Publishing Company.