Analytic Function

An analytic function is a type of mathematical function that is smooth and well-behaved, meaning it can be differentiated (or "brought down" to a lower level) repeatedly everywhere in its domain. These functions can be expanded into power series, like an infinite sum of terms, around any point within their region of definition. Their predictable and stable nature makes them important in fields like physics and engineering, where they help model and analyze complex systems smoothly and accurately. Essentially, analytic functions are those that exhibit a high level of mathematical "niceness" and consistency throughout their entire domain.