Waring’s formula

Let x1,,xn be n indeterminates. For k1, let σk be the kth elementary symmetric polynomials in x1,,xn, and Sk be the kth power sum defined as


Like the Newton’s formula, the Waring formulaMathworldPlanetmath is a relation between σk and Sk:


where the summation is over all n-tuples (i1,,in)n with non-negative components, such that


In particular, when there are two indeterminates, i.e. n=2, the Waring formula reads

Title Waring’s formula
Canonical name WaringsFormula
Date of creation 2013-03-22 15:34:26
Last modified on 2013-03-22 15:34:26
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 9
Author alozano (2414)
Entry type Theorem
Classification msc 11C08
Synonym Waring formula
Related topic NewtonGirardFormulaSymmetricPolynomials