Measured Multiseries and Integration

Abstract

A paper by Bruno Salvy and the author introduced measured multiseries and gave an algorithm to compute these for a large class of elementary functions, modulo a zeroequivalence method for constants. This gave a theoretical background for the Maple c implementation that Salvy was developing at that time.The main result of the present article is an algorithm to calculate measured multiseries for integrals of the form h sin G, where h and G belong to a Hardy field, H. The process can reiterated with the resulting algebra, and also applied to solutions of a second order differential equation of a particular form.