Construction a novel generating functions for the products of certain numbers and orthogonal polynomials in several variables using the symmetric functions technique

In this paper, we introduce novel generating functions of the products of k-Fibonacci numbers, k-Lucas numbers, k-Pell numbers, k-Jacobsthal numbers, k-Mersenne numbers and symmetric functions in multiple variables. Accordingly, the novel generating functions are assigned to the other orthogonal Chebyshev polynomials with symmetric functions in multiple variables.

Keywords:

Symmetric functions , Generating functions , k-Fibonacci numbers , k-Lucas numbers , k-Pell numbers , k-Mersenne numbers , Chebishev polynomials