Symmetric functions of binary products of bivariate complex Lucas polynomials and some special numbers and polynomials

Abstract

In this paper, we introduce an operator in order to derive some new symmetric properties of bivariate complex Lucas polynomials, then we give some new generating functions of the products of bivariate complex Lucas polynomials with Chebyshev polynomials of the first, second, third and fourth kinds, k-Fibonacci numbers, k-Lucas numbers, k-Pell numbers, k-Pell Lucas numbers, k-Jacobsthal numbers and k-Jacobsthal Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions of the products of bivariate complex Lucas polynomials with Fibonacci polynomials, Pell polynomials and Jacobsthal polynomials.