The asymptotic behaviour of many univariate functions can only be expressed in generalized asymptotic scales, which are not merely formed of powers of a single variable. The computation of asymptotic expansions of functions in such generalized scales may lead to infinite cancellations, which complicate the design and implementation of practical algorithms. In this paper, we introduce a new heuristic technique of “meta-expansions”, which is both simple and efficient in practice, even though the answers are not guaranteed to be correct in general.

Keywords: transseries, asymptotic expansion, algorithm, zero-test

A.M.S. subject classification: 40-04, 41A60, 68W30, 03C64, 03D60, 65B99

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