Definition:Interval of Convergence
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Definition
Let $\xi \in \R$ be a real number.
Let $\ds \map S x = \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$ 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
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 20$: Taylor Series for Functions of One Variable
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 15.2$