English

Transseries for beginners

Rings and Algebras 2010-11-08 v5 Classical Analysis and ODEs History and Overview

Abstract

From the simplest point of view, transseries are a new kind of expansion for real-valued functions. But transseries constitute much more than that--they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries is a large ordered field, extending the real number field, and endowed with additional operations such as exponential, logarithm, derivative, integral, composition. Over the course of the last 20 years or so, transseries have emerged in several areas of mathematics: asymptotic analysis, model theory, computer algebra, surreal numbers. This paper is an exposition for the non-specialist mathematician. All a mathematician needs to know in order to apply transseries.

Keywords

Cite

@article{arxiv.0801.4877,
  title  = {Transseries for beginners},
  author = {G. A. Edgar},
  journal= {arXiv preprint arXiv:0801.4877},
  year   = {2010}
}

Comments

53 pages

R2 v1 2026-06-21T10:08:16.491Z