Summary processes - Asymptotic developments

When dealing with a sum, whether finite or infinite, boundary-dependent or parameter-dependent, we are often only interested in its behavior in the vicinity of a particular point, at finite or infinite distance. This requires asymptotic evaluation methods. We begin by introducing the language of asymptotic comparison, which is ubiquitous in analysis. Then we'll look at some fairly general methods, illustrated by examples. In many cases, these procedures lead to rather complicated calculations, which formal calculus software is not always capable of performing at present.