Accelero-summation of the formal solutions of nonlinear difference equations
type: Item
instance of: scholarly article
title: Accelero-summation of the formal solutions of nonlinear difference equations
zbMATH Open document ID: 1225.39005
author: Geertrui Klara Immink
publication date: 2011-05-26T00:00:00Z
full work available at URL: https://eudml.org/doc/219670
full work available at URL: AIF 2011 61 1 1 0.pdf
review text: The author studies the following nonlinear difference equation \[ y\left( z+1\right) =z^{\lambda /p}F\left( z^{1/p},y\left( z\right) \right) , \tag{1} \] where \(p\in \mathbb{N}\), \(\lambda \in \mathbb{Z}\) and \(F\) is a \(\mathbb{C} ^{n}\)-valued function, analytic in a neighbourhood of \(\left( \infty ,y_{0}\right) \) for some \(y_{0}\in \mathbb{C}^{n}\). The main result shows that the formal solution of (1) is accelero-summable (in some weaker form than given by \textit{B.~L.~J. Braaksma, B. F. Faber} and \textit{G. K. Immink} [Pac. J. Math. 195, No.~1, 35--65 (2000; Zbl 1008.39003)]), even \(0\) is a singular direction of level \(1\).
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A45
Mathematics Subject Classification ID: 40G10
Mathematics Subject Classification ID: 32A05
zbMATH DE Number: 5899946
zbMATH Keywords: nonlinear difference equation
zbMATH Keywords: formal solution
zbMATH Keywords: accelero-summation
zbMATH Keywords: quasi-function
MaRDI profile type: Publication
OpenAlex ID: W2565020691
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DOI: 10.5802/AIF.2596
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5899946