Asymptotic Expansions for Sub-Critical Lagrangean Forms

Authors Hsien-Kuei Hwang , Mihyun Kang , Guan-Huei Duh

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Author Details

Hsien-Kuei Hwang
  • Institute of Statistical Science, Academia Sinica, Taiwan
Mihyun Kang
  • Institute of Discrete Mathematics, TU Graz, Austria
Guan-Huei Duh
  • Institute of Statistical Science, Academia Sinica, Taiwan

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Hsien-Kuei Hwang, Mihyun Kang, and Guan-Huei Duh. Asymptotic Expansions for Sub-Critical Lagrangean Forms. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Asymptotic expansions for the Taylor coefficients of the Lagrangean form phi(z)=zf(phi(z)) are examined with a focus on the calculations of the asymptotic coefficients. The expansions are simple and useful, and we discuss their use in some enumerating sequences in trees, lattice paths and planar maps.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Generating functions
  • Mathematics of computing → Enumeration
  • asymptotic expansions
  • Lagrangean forms
  • saddle-point method
  • singularity analysis
  • maps


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