Irrational sums
type: Item
instance of: scholarly article
title: Irrational sums
zbMATH Open document ID: 0852.11034
author: Yanyan Li
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-12-05T00:00:00Z
review text: Sufficient conditions for the irrationality of the sum of the series \(\sum_{n\geq 1} 1/H (f(n))\) are obtained. Here \(H(k)\) is a recurrent sequence and \(f\) is a strictly increasing function from the set of positive integers to the set of nonnegative integers. All the proofs are based on an elementary irrational criterion due to the reviewer [Glasg. Math. J. 29, 221-228 (1987; Zbl 0629.10027)]. Several analogous results are now known, due to the work of P.-G. Becker, P. Bundschuh, P. Hančl, P. Kiss, W. McDaniel, A. Pethö, T. Töpfer, K. Väänänen and the reviewer, among others.
Mathematics Subject Classification ID: 11J72
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 894647
zbMATH Keywords: irrationality
zbMATH Keywords: recurrent sequence
reviewed by: Cătălin Badea
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072142
OpenAlex ID: W4254175449
cites work: The irrationality of certain infinite series
cites work: Q3872528
cites work: Q3916657
cites work: An irrational sum
cites work: A remark on a result of L. Kuipers
cites work: Q3720486
DOI: 10.1216/RMJM/1181072142
description: scientific article; zbMATH DE number 894647