Definition:Power Sum
Jump to navigation
Jump to search
Definition
Let $S$ be a finite set of numbers.
Let $p \in \R$ be a real number.
Then the $p$th power sum of $S$ is defined as:
- $S_p = \ds \sum_{x \mathop \in S} x^p$
That is, it is the summation of the $p$th powers of all the elements of $S$.
Also defined as
Most sources define $S$ as a set indexed by $\left\{ {1, 2, \ldots n}\right\}$ or $\left\{ {0, 1, \ldots n}\right\}$, and denote $S_p$ as:
- $S_p = \ds \sum_{j \mathop = 1}^n {x_j}^p$
or:
- $S_p = \ds \sum_{j \mathop = 0}^n {x_j}^p$
accordingly.
Some sources, depending upon the direction they are taking their arguments, restrict $p$ to the set $\Z_{>0}$ of (strictly) positive integers.
Sources
- Weisstein, Eric W. "Power Sum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PowerSum.html