Analytic continuity refers to a property of functions in mathematics, particularly in complex analysis. A function is said to be analytically continuous if it can be represented by a power series in a neighborhood around every point in its domain. This means that the function behaves smoothly and predictably, without any abrupt changes or discontinuities. In simpler terms, if you can draw a function without lifting your pencil, it is likely to be analytically continuous. This concept is crucial for understanding how functions behave and interact, especially in fields like calculus and complex analysis, where the study of holomorphic functions relies on this property.