Newton identities
= Newton identities
{c}
{wiki=Newton's_identities}
Newton's identities relate the elementary symmetric polynomials $e_k$ to the power sums $p_k=\sum_i x_i^k$. The first three give
$$
e_1=p_1,
\qquad
2e_2=p_1^2-p_2,
\qquad
6e_3=p_1^3-3p_1p_2+2p_3.
$$