Real Analysis Exchange

Transseries for Beginners

G. A. Edgar

Full-text: Open access

Abstract

From the simplest point of view, transseries concern manipulations on formal series, or 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---also known as the transline---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: dynamical systems, 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.

Article information

Source
Real Anal. Exchange, Volume 35, Number 2 (2009), 253-310.

Dates
First available in Project Euclid: 22 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.rae/1285160533

Mathematical Reviews number (MathSciNet)
MR2683600

Zentralblatt MATH identifier
1218.41019

Subjects
Primary: 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 30A84

Keywords
Hardy field ordered field differential field log-exp series Ecalle

Citation

Edgar, G. A. Transseries for Beginners. Real Anal. Exchange 35 (2009), no. 2, 253--310. https://projecteuclid.org/euclid.rae/1285160533


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