Holomorphic functions

Holomorphic functions are complex functions that are differentiable everywhere in their domain, meaning they have a well-defined derivative at every point. This property ensures the function behaves smoothly and predictably, with no abrupt changes. In simpler terms, holomorphic functions are the “well-behaved” functions of complex analysis, often exhibiting interesting properties like infinite differentiability and being representable by power series. They play a central role in various fields of mathematics and physics because of their smoothness and the rich structure they possess in the complex plane.