Asymptotic expansion is a mathematical technique used to describe the behavior of functions as they approach a particular limit, often infinity. It provides an approximation of a function by expressing it as a series of simpler functions, which become increasingly accurate as the variable approaches the limit. This method is particularly useful in fields like mathematics, physics, and engineering. In an asymptotic expansion, the leading term gives the dominant behavior of the function, while subsequent terms refine the approximation. This approach helps in analyzing complex problems where exact solutions are difficult to obtain, making it a valuable tool in applied mathematics and numerical analysis.