A generalization of Euler's constant
type: Item
instance of: scholarly article
title: A generalization of Euler's constant
zbMATH Open document ID: 1130.11075
author: Alina Sîntămărian
published in: Numerical Algorithms
publication date: 2007-12-17T00:00:00Z
review text: As a generalization of the Euler's constant \(\gamma\), the author considers the series \[ \gamma(a)= \lim_{n\rightarrow\infty} \sum_{i=1}^n 1/(a+i-1)- \ln((a+n-1)/a) \quad\text{for }a>0; \] first she proves that \(\gamma(a)\) is a decreasing function of \(a\) and then she gives some related sequences, comparable by \(\gamma(a)\) and useful to evaluate it. Reviewer's remark: As I know, there are various generalizations of the Euler's constant. For example, see \textit{J. Sondow} and \textit{P. Hadjicostas}, J. Math. Anal. Appl. 332, No. 1, 292--314 (2007; Zbl 1113.11017) and \textit{M. Spreafico}, Funkts. Anal. Prilozh. 39, No. 2, 87--91 (2005; Zbl 1115.33002).
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 11Y60
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A06
zbMATH DE Number: 5220696
zbMATH Keywords: Euler's constant
zbMATH Keywords: inequality
zbMATH Keywords: series
MaRDI profile type: Publication
full work available at URL: s11075-007-9132-0
OpenAlex ID: W1996624435
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DOI: 10.1007/S11075-007-9132-0
description: scientific article