Fast computation of some asymptotic functional inverses
type: Item
instance of: scholarly article
title: Fast computation of some asymptotic functional inverses
zbMATH Open document ID: 0840.11052
author: Bruno Salvy
published in: Journal of Symbolic Computation
publication date: 1996-07-01T00:00:00Z
review text: \textit{G. Robin} [Publ. Inst. Math., Nouv. Sér. 43, 17-25 (1988; Zbl 0655.10040)] showed that in some asymptotic expansions of the form \(y(x)\approx \sum_n P_n(\log\log x)/\log^n x\), the polynomial \(P_n\) satisfies a simple iterative relation. However, his result cannot be used to compute \(P_n\) for want of the value of the constant term in the relation. Here, the author gives a new derivation of some of Robin's results and shows how the constant term can be computed by the manipulation of formal power series. The new scheme now enables one to compute the polynomials \(P_n\) efficiently.
Mathematics Subject Classification ID: 11Y35
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 638316
zbMATH Keywords: asymptotic functional inverses
zbMATH Keywords: asymptotic expansions
reviewed by: Peter Shiu
MaRDI profile type: Publication
OpenAlex ID: W2041039575
DOI: 10.1006/JSCO.1994.1014
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description: scientific article; zbMATH DE number 638316