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Asymptotic expansions of logarithmic-exponential functions

Asymptotic expansions of logarithmic-exponential functions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Asymptotic expansions of logarithmic-exponential functions

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s005740200005
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Apr 1, 2002

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