Asymptotic expansions of logarithmic-exponential functions

Ferte, Damien
April 2002
Bulletin of the Brazilian Mathematical Society;Apr2002, Vol. 33 Issue 1, p125
Academic Journal
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 (Parusinski). 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.


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