Complete and elementary symmetric functions in several variables and orthogonal polynomials

Hassina Zerroug; Ali Boussayoud; Abdelhamid Abderrezzak; Mohamed Kerada

Hassina Zerroug Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria
Ali Boussayoud LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria
Abdelhamid Abderrezzak University of Paris 7LITP, Place Jussieu Paris cedex 05, France
Mohamed Kerada Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria

Abstract

In this paper, we first derive some new generating functions of the products of k-Fibonacci numbers, k-Lucas numbers, k-Pell numbers, k-Jacobsthal numbers, Mersenne numbers and symmetric function in several variables . After that, we give the new generating functions for products of the other ortogonal Chebyshev polynomials with symmetric function in several variables.