Fast computation of some asymptotic functional inverses
\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.
scientific article; zbMATH DE number 638316