On the computation of limsups

[摘要] In the last years, several asymptotic expansion algorithms have appeared, which have the property that they can deal with very general types of singularities, such as singularities arising in the study of algebraic differential equations. However, attention has been restricted so far to functions with ''strongly monotonic'' asymptotic behaviour: formally speaking, the functions lie in a common Hardy field, or, alternatively, they are determined by transseries. In this article, we make a first step towards the treatment of functions involving oscillatory behaviour. More precisely, let phi be an algebraic function defined on [-1, 1](q), let F-1(x),...,F-q(x) be exp-log functions at infinity in x, and let psi(x) = phi(sin(F-1(x)),...,sin(F-q(x))). We give a method to compute lim sup(x-->infinity) psi(x). Moreover, the techniques we use are stronger than this result might suggest, and we outline further applications. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-05-01

[效力级别]  Proceedings Paper