On the New Families of k− Pell Numbers and k− Pell-Lucas Numbers and Their Polynomials

We introduce advances in the study of k−Pell and k−Pell-Lucas numbers. Then we give some properties of these families and find the generating functions of the families for some k. In addition, we identify the relationships between the family of k−Pell numbers and the classical Pell numbers as well as the family of k−Pell-Lucas numbers and the classical Pell-Lucas numbers. Further, we define generalized polynomials for these numbers. We also obtain some useful properties of these polynomials. Additionally, we give the relationships between the generalized k−Pell polynomials and the classical Pell polynomials as well as the generalized k−Pell-Lucas polynomials and the classical Pell-Lucas polynomials. These generalizations are given in matrix representation. Results in this paper include Cassini identities for these families and polynomials. © 2011 JCAM All rights reserved.