Definition:Interval of Convergence

Definition

Let $\xi \in \R$ be a real number.

Let $\displaystyle S \paren x = \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$ be a power series in $x$ about $\xi$.

Then the set of values of $x$ for which $S \paren x$ converges is called the interval of convergence of $S$.