For three variables, α‎, β‎, γ‎, the elementary symmetric polynomials are

These expressions generalize naturally to n variables, with σ‎_k being the sum of the $\left(\begin{array}{c}n\\ k\end{array}\right)$ products of k of the variables. The elementary symmetric polynomials appear in Viète’s formulae.

The elementary symmetric polynomials are symmetric functions, and any symmetric polynomial can be expressed in terms of the elementary symmetric polynomials. For example, if s_k = α‎^k + β‎^k + γ‎^k, then

gives a general recursive means of expressing s_k in terms of σ‎₁,σ‎₂,…,σ‎_k. See Newton’s identities.