Hermite-Padé approximants to exponential functions and an inequality of Mahler
type: Item
instance of: scholarly article
title: Hermite-Padé approximants to exponential functions and an inequality of Mahler
zbMATH Open document ID: 0937.11028
author: F. Wielonsky
published in: Journal of Number Theory
publication date: 2000-06-13T00:00:00Z
review text: The main results of this paper are that the inequalities \[ |e^q-a|> q^{-19.183q} \quad\text{and}\quad |\log q-a|> q^{-19.183\log \log q} \] hold for every large positive integer \(q\) and \(a\). The proofs are based on using suitable approximation of Legendre-type polynomials. The method is similar to Hermite-Padé approximation.
Mathematics Subject Classification ID: 11J17
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 1271090
zbMATH Keywords: exponential function
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: diophantine approximation
zbMATH Keywords: Legendre-type polynomials
zbMATH Keywords: Hermite-Padé approximation
reviewed by: Jaroslav Hančl
MaRDI profile type: Publication
full work available at URL: jnth.1998.2334
OpenAlex ID: W2051279854
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DOI: 10.1006/JNTH.1998.2334
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description: scientific article; zbMATH DE number 1271090