A particular type of summability of divergent power series, with an application to difference equations

G.K. Immink

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3 Citations (Scopus)

Abstract

We define a "weak Borel-sum" for a class of formal power series. This is a generalization of the ordinary Borel-sum with applications in the theory of locally analytic difference equations. We explain its relation to a particular type of accelerosum obtained by the use of a weak acceleration operator, and briefly discuss a corresponding Stokes phenomenon. Most results of this paper are based on the quasi-analyticity of a certain type of Borel transform.

Original languageEnglish
Pages (from-to)123-148
Number of pages26
JournalAsymptotic Analysis
Volume25
Issue number2
Publication statusPublished - Feb-2001

Keywords

  • FORMAL SOLUTIONS
  • MULTISUMMABILITY
  • SUMMATION

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