Asymptotic expansions
David F. Andrews, James E. Stafford · 2000
Abstract The technical objective of an asymptotic analysis involving expansions is the determination of the terms /?O. g 1 • . . . The rationa1es for examining these terms and their interpretation are varied and of primary importance. While deriving these terms is a necessary part of the process, it is, in a sense, the easiest part. Unfortunately, it is often not easy and the algorithms of this chapter are an attempt to alleviate this difficulty. There is no guarantee that an expansion is valid or that the results will be useful. We fol1ow the tradition, long established in computing, and assume that the user knows what s/he wants to compute and wishes to do it correctly and efficiently. The computations associated with asymptotic expansions may be broken down into a small number of basic procedures or rules.