analytic behavior - перевод на русский

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. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about ${\displaystyle x_{0}}$ converges to the function in some neighborhood for every ${\displaystyle x_{0}}$ in its domain.