analytic functions

Analytic functions are mathematical functions that have a special property: they can be represented by power series within a certain range. This means they are smooth and continuous, with no abrupt changes or breaks. In simpler terms, if you were to graph an analytic function, it would create a smooth curve without any jumps. These functions are essential in complex analysis, a branch of mathematics that studies functions of complex numbers, and they are used in various fields, including engineering, physics, and economics, to model behaviors and solve problems efficiently.