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

Article type: Research Article

Authors: Immink, G.K.

Affiliations: Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands

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 accelero‐sum 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.

Journal: Asymptotic Analysis, vol. 25, no. 2, pp. 123-148, 2001