Generating functions of binary products of k-Fibonacci and orthogonal polynomials

Abstract

In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Pell numbers and Tchebychev polynomials of first and second kind. By making use of the new operator defined in this paper, we give some new generating functions for k-Fibonacci and k-Pell numbers and Fibonacci polynomials.