Abstract:
In this paper, we generalize the known Gauss Pell-Lucas numbers, and call such
numbers as the generalized Gauss k-Pell-Lucas numbers. We obtain relations between
the family of the generalized Gauss k-Pell-Lucas numbers and the known
Gauss Pell-Lucas numbers. We generalize the known Gauss Pell-Lucas polynomials,
and call such polynomials as the generalized Gauss k-Pell-Lucas polynomials.
We obtain relations between the family of the generalized Gauss k-Pell-Lucas polynomials
and the known Gauss Pell-Lucas polynomials. In addition, we present the
new generalizations of these numbers and polynomials in matrix form. Then, we
get Cassini’s identities for these numbers and polynomials.