Asymptotics

Abstract

While in St Andrews in the early 1960s, I learned from Bob Dingle about his theory of the high orders of divergent series. This inspired an enthusiasm for asymptotics, but I did not then realise how seminal his achievements were. Indeed, for two decades afterwards, I declared myself as a ‘first terms asymptotist’, arguing that high orders are unnecessary: getting the leading order right, as in the uniform approximations near caustics (Chapter 2) is accurate enough for most applications.