A recursion formula for the coefficients in an asymptotic expansion

Abstract

Many authors have proved results deducing an asymptotic expansion offor large from the behaviour of f(t), when f(t) is regular in an appropriate part of the complex t-plane. For example, if, for some k > 0 and some Am, αmfor all large such that R(t) > C, then, as ⃗ ∞ in a suitable sector in the z-plane, we havewhere Z is an appropriate value of z1/z.