Notes on particular symmetric polynomials with applications

This paper presents some applications using several properties of three important symmetric polynomials: elementary symmetric polynomials, complete symmetric polynomials and the power sum symmetric polynomials. The applications includes a simple proof of El-Mikkawy conjecture in [M.E.A. El-Mikkawy, Appl. Math. Comput. 146 (2003) 759–769] and a very easy proof of the Newton–Girard formula. In addition, a generalization of Stirling numbers is obtained.