Definition:Power Series/Center
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This page is about Center in the context of Power Series. For other uses, see 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.
Sources
- 1992: Larry C. Andrews: Special Functions of Mathematics for Engineers (2nd ed.) ... (previous) ... (next): $\S 1.3.2$: Power series: $(1.39)$