What is "analytic function"

n. (context analysis English) a real valued function which is uniquely defined through its derivatives at one point

In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not hold generally for real analytic functions. A function is analytic if and only if its Taylor series about x converges to the function in some neighborhood for every x in its domain.