On the computation of the Euler constant \({\gamma}\)
type: Item
instance of: scholarly article
title: On the computation of the Euler constant \({\gamma}\)
zbMATH Open document ID: 0958.33001
DOI: 10.1023/A:1019137125281
author: E. A. Karatsuba
published in: Numerical Algorithms
publication date: 2000-11-22T00:00:00Z
review text: Let \(H(n)=n^2 \Bigl[1+{1 \over 2}+ \cdots+ {1\over n}-\log \Bigl( n+ {1\over 2}\Bigr) -C\Bigr],\) where \(C\) is the Euler constant. The author proves a conjecture of Matti Vuorinen which states that \(H(n)\) increases monotonically from \(H(1)=0.0173 \dots\) to \(\lim_{n\to \infty} H(n)=1/24= 0.0416 \dots\) \((n=1,2,3, \dots)\). There appear also some new formulas for the computation of \(C\).
reviewed by: József Sándor
Mathematics Subject Classification ID: 11Y60
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 68Q30
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 1534765
zbMATH Keywords: Euler's constant
zbMATH Keywords: gamma function
zbMATH Keywords: Stirling's formula
Wikidata QID: Q61772971
MaRDI profile type: Publication
DBLP publication ID: journals/na/Karatsuba00
description: scientific article; zbMATH DE number 1534765