Asymptotic solutions of the translation equation
type: Item
instance of: scholarly article
title: Asymptotic solutions of the translation equation
zbMATH Open document ID: 0831.39007
DOI: 10.1007/BF03323040
author: Detlef Gronau
author: Lothar Berg
published in: Results in Mathematics
publication date: 1996-02-20T00:00:00Z
review text: The authors deal with asymptotic developments of solutions \(F(x,t)\) of the translation equation \(F(x,s+t)=F(F(x,s), t)\). They consider asymptotic formulas for \(F(x, u/x^m) \approx \sum^\infty_{n=1} f_n (u)x^n\) when \(x \to+0 (- 0)\) for fixed \(u\) and \(m \in \mathbb{N}\). Using these results they also consider asymptotic expansions \(F(x,t)=\sum^\infty_{n=1} \sum^{n-1}_{\nu=1} a_{n \nu} (x) \ln^\nu (t)t^{-n}\) for \(t \to \infty\). There is also a discussion about using Lie series for their purpose. Moreover several examples are given.
reviewed by: Jens Schwaiger
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 785162
zbMATH Keywords: translation equation
zbMATH Keywords: asymptotic formulas
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: Lie series
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03323040
OpenAlex ID: W1984642186
description: scientific article; zbMATH DE number 785162