K-pell numbers and polynomials

In this thesis, a new family of k-Pell numbers has been defined. Then the generating function of the new family has been found for k=2. The relationship between the family of k-Pell numbers and the known Pell numbers has been given. Also the polynomials of k-Pell numbers have been defined. Some interesting properties of the polynomials has been given. The relationship between k- Pell polynomials and known Pell polynomials. Lastly, the new generalizations of these families and the polynomials in matrix representation have been found.