analytic function in Portuguese

(analysis) Any smooth (infinitely differentiable) function f, defined on an open set D\subseteq \mathbb{C}\ (\textit{ or }\subseteq\mathbb{R}), whose value in some neighbourhood of any given point x_0 \in D is given by the Taylor series \textstyle \sum_{n=0}^{\infty} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^{n}.