@article{Arafat2024, 
author = {Ahmed Arafat and Moawwad El-Mikkawy},
title = {Novel identities for elementary and complete symmetric polynomials with diverse applications},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {23489-23511},
keywords = {elementary symmetric polynomials, complete symmetric polynomials, Schur convexity, Vandermonde matrix, tri-diagonal matrix, Jacobi polynomials},
url = {https://www.sciopen.com/article/10.3934/math.20241142},
doi = {10.3934/math.20241142},
abstract = {This article aims to present novel identities for elementary and complete symmetric polynomials and explore their applications, particularly to generalized Vandermonde and special tri-diagonal matrices. It also extends existing results on Jacobi polynomials  Pn(α,β)(x) and introduces an explicit formula based on the zeros of  Pn−1(α,β)(x). Several illustrative examples are included.}
}