Newton 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}, 2 e_{2} = p_{1}^{2} - p_{2}, 6 e_{3} = p_{1}^{3} - 3 p_{1} p_{2} + 2 p_{3} .

 Ancestors (6)