Transseries for Beginners

G. A. Edgar

Real Analysis Exchange

35 (2010) 253-310

G. A. Edgar
Department of Mathematics
The Ohio State University
Columbus, OH 43210   U.S.A.     
edgar@math.ohio-state.edu

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 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.

download PDF file:

[PDF] beginners.pdf   (version of June, 2010)

arXiv   (previous versions)

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