The Hardy-Littlewood function: an exercise in slowly convergent series
type: Item
instance of: scholarly article
title: The Hardy-Littlewood function: an exercise in slowly convergent series
zbMATH Open document ID: 1066.40003
author: Walter Gautschi
published in: Journal of Computational and Applied Mathematics
publication date: 2005-06-01T00:00:00Z
review text: Two procedures for computing the values of the Hardy-Littlewood function \[ H(x)=\sum_{k=1}^{\infty}\frac{1}{k}\sin \frac{x}{k} \] are presented. The first one is based on Gaussian quadrature, while the second method uses direct summation for the first \(n\) terms of the series, where \(n\approx x\), in combination with some well-known formulae for zeta functions. Such calculations are of interest for exploring the possible boundedness of \(H\) from above and from below.
reviewed by: Vasile Berinde
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 2173197
zbMATH Keywords: Gauss quadrature
zbMATH Keywords: summation
describes a project that uses: GQRAT
MaRDI profile type: Publication
full work available at URL: j.cam.2004.09.043
OpenAlex ID: W2073279886
cites work: Q5558293
cites work: On a conjecture of Clark and Ismail
cites work: Q4284658
cites work: Q5690368
cites work: Algorithm 793
cites work: Gaussian Quadrature Involving Einstein and Fermi Functions with an Application to Summation of Series
cites work: Notes on the Theory of Series (XX): On Lambert Series
DOI: 10.1016/J.CAM.2004.09.043
description: scientific article; zbMATH DE number 2173197