analytic function

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|analysis}} Any [[smooth]] (infinitely differentiable) [[function]] <math>f</math>, defined on an [[open set]] {{C|en|Functions}} <math>D\subseteq \mathbb{C}\ (\textit{ or }\subseteq\mathbb{R})</math>, whose value in some [[neighbourhood]] of any given point <math>x_0 \in D</math> is given by the [[Taylor series]] <math>\textstyle \sum_{n=0}^{\infty} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^{n}</math>.
2. {{lb|en|databases}} [[window function]]

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