Introduction

Abstract

This book is about the automatic computation of asymptotic behaviour of functions of a real variable, x. This means that we shall wish to compute limits, and also to give some measure of how rapidly a given function approaches its limit Throughout, we shall assume that our interest is in the behaviour as x → ∞. This is for convenience only, since other cases can be considered by using a transformation of one of the forms x → ±(x – x ₀)^-1. These give separate treatments of the cases when x tends to x ₀ from above and below. We shall want our methods to be at least potentially implementable, and we shall, from time to time, give some consideration to actual implementations. However this book is really about algorithms and the mathematical principles that underlie them, rather than details of implementation.