Definition:Interval of Convergence

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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


Sources