# Definition:Power Series/Center

## Definition

Let $\ds \sum_{n \mathop = 0}^\infty a_n \size {x - \xi}^n$ be a power series.

The point $\xi$ is the center of $\ds \sum_{n \mathop = 0}^\infty a_n \size {x - \xi}^n$.

## Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.