Definition:Interval of Convergence

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

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

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

Also see

 * Existence of Interval of Convergence of Power Series