Asymptotic expansions of logarithmic-exponential functions

  • Rémi Soufflet


The aim of this paper is to study the asymptotic expansion of real functions which are finite compositions of globally subanalytic maps with the exponential function and the logarithmic function. This is done thanks to a preparation theorem in the spirit of those that exist for analytic functions (Weierstrass) or subanalytic functions (Parusinśki). The main consequence is that logarithmic-exponential functions admit convergent asymptotic expansion in the scale of real power functions. We also deduce a partial answer to a conjecture of van den Dries and Miller.

Keywords: preparation theorem, asymptotic expansions, Hardy fields. 
Mathematical subject classification: 32B15, 32B20, 34E05. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Sociedade Brasileira de Matemática 2002

Authors and Affiliations

  • Rémi Soufflet
    • 1
  1. 1.Université de Bourgogne, Laboratoire de Topologie, UMR 5584, UFR des Sciences et Techniques, 9 avenue Alain Savary, B.P. 47870 - 21078 Dijon, Cedex, FRANCE E-mail: soufflet@topolog.u-bourgogne.frBrazil

Personalised recommendations