Topic
series which gives an approximation to a function as the argument tends to some point
In mathematics, an asymptotic expansion, asymptotic series, or Poincaré expansion is a formal series used to approximate a given function near a specific point or at infinity. The term asymptotic series is commonly reserved for a divergent series whose terms initially decrease to a minimum magnitude and then increase without bound. Although divergent, the truncated series provides an approximation with increasing accuracy as the function's argument approaches the asymptotic limit. These expansions are useful when a standard Taylor series converges too slowly, as an asymptotic series can often give high accuracy with only a few terms. An asymptotic expansion depends on the domain and limit point. A function of a real variable may require distinct series near the origin versus at infinity. An entire function of a complex variable may require distinct asymptotic series for different sectors of the complex plane, a behavior called the Stokes phenomenon.
