Measured Multiseries and Integration

TL;DR

This paper develops an algorithm to compute measured multiseries for integrals of functions involving Hardy field elements, extending previous work and enabling iterative analysis of such integrals and solutions to specific differential equations.

Contribution

It introduces a new algorithm for calculating measured multiseries of integrals of functions like h*sin G, where h and G are in a Hardy field, expanding the theoretical framework.

Findings

Algorithm successfully computes measured multiseries for specified integrals.

Method can be iterated with the algebra of measured multiseries.

Applicable to solutions of certain second order differential equations.

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 zero-equivalence method for constants. This gave a theoretical background for the 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 functions of the form h*sin G, where h and G belong to a Hardy field. The process can reiterated with the resulting algebra, and also applied to solutions of a second order differential equation of a particular form.