asymptotic expansions

An asymptotic expansion is a way to approximate a complex function by expressing it as a series of simpler terms that become more accurate as a variable approaches a certain limit, often zero or infinity. Think of it as a detailed roadmap showing how the function behaves near that limit, focusing on the most significant contributions first. While these series may not converge to the exact function everywhere, they provide highly useful approximations for understanding and calculating the function's behavior in those extreme regions, especially in fields like mathematics, physics, and engineering.