There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1, ..., x_n) = sum_(k = 1)^n x_k^p, and the second is the special case x_k = k, i.e., S_p(n) = sum_(k = 1)^n k^p. General power sums arise commonly in statistics. For example, k-statistics are most commonly defined in terms of power sums. Power sums are related to symmetric polynomials by the Newton-Girard formulas.

Diophantine equation | Faulhaber's formula | multigrade equation | Nicomachus's theorem | series | sum