Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 10 2023 10 01 Construction a novel generating functions for the products of certain numbers and orthogonal polynomials in several variables using the symmetric functions technique 179 198 7948 10.22075/ijnaa.2023.29432.4163 EN Sana Sana Krioui Mathematics Faculty, Department of Algebra and Number Theory, LATN Laboratory, USTHB, BP32, Bab Ezzouar, Algiers, Algeria Ali Boussayoud LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria Abdelaziz Abdelaziz Bellagha Mathematics Faculty, Department of Algebra and Number Theory, LATN Laboratory, USTHB, BP32, Bab Ezzouar, Algiers, Algeria Journal Article 2023 01 05 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. Symmetric functions Generating functions k-Fibonacci numbers k-Lucas numbers k-Pell numbers k-Mersenne numbers Chebishev polynomials https://ijnaa.semnan.ac.ir/article_7948_19689efbe009d4ff5579d772f2bcc5be.pdf