Open Access
2009/2010 Transseries for Beginners
G. A. Edgar
Real Anal. Exchange 35(2): 253-310 (2009/2010).


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.


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G. A. Edgar. "Transseries for Beginners." Real Anal. Exchange 35 (2) 253 - 310, 2009/2010.


Published: 2009/2010
First available in Project Euclid: 22 September 2010

zbMATH: 1218.41019
MathSciNet: MR2683600

Primary: 03C60 , 30A84 , 41A60

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

Rights: Copyright © 2009 Michigan State University Press

Vol.35 • No. 2 • 2009/2010
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