A new sequence related to the Euler–Mascheroni constant

Abstract In this paper, we provide a new quicker sequence convergent to the Euler–Mascheroni constant using an approximation of Padé type. Our sequence has a relatively simple form and higher speed of convergence. Moreover, we establish lower and upper bound estimates for the difference between the...

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Main Authors:	Shanhe Wu, Gabriel Bercu
Format:	Article
Language:	English
Published:	SpringerOpen 2018-06-01
Series:	Journal of Inequalities and Applications
Subjects:	Sequences Euler–Mascheroni constant Rate of convergence Lower and upper bounds
Online Access:	http://link.springer.com/article/10.1186/s13660-018-1746-3

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spelling	doaj-ccb5b86ab21144adab24cf42c8d8875e2020-11-24T20:53:31ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-06-012018111210.1186/s13660-018-1746-3A new sequence related to the Euler–Mascheroni constantShanhe Wu0Gabriel Bercu1Department of Mathematics, Longyan UniversityDepartment of Mathematics and Computer Sciences, “Dunărea de Jos” University of GalaţiAbstract In this paper, we provide a new quicker sequence convergent to the Euler–Mascheroni constant using an approximation of Padé type. Our sequence has a relatively simple form and higher speed of convergence. Moreover, we establish lower and upper bound estimates for the difference between the sequence and the Euler–Mascheroni constant.http://link.springer.com/article/10.1186/s13660-018-1746-3SequencesEuler–Mascheroni constantRate of convergenceLower and upper bounds
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Shanhe Wu Gabriel Bercu
spellingShingle	Shanhe Wu Gabriel Bercu A new sequence related to the Euler–Mascheroni constant Journal of Inequalities and Applications Sequences Euler–Mascheroni constant Rate of convergence Lower and upper bounds
author_facet	Shanhe Wu Gabriel Bercu
author_sort	Shanhe Wu
title	A new sequence related to the Euler–Mascheroni constant
title_short	A new sequence related to the Euler–Mascheroni constant
title_full	A new sequence related to the Euler–Mascheroni constant
title_fullStr	A new sequence related to the Euler–Mascheroni constant
title_full_unstemmed	A new sequence related to the Euler–Mascheroni constant
title_sort	new sequence related to the euler–mascheroni constant
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2018-06-01
description	Abstract In this paper, we provide a new quicker sequence convergent to the Euler–Mascheroni constant using an approximation of Padé type. Our sequence has a relatively simple form and higher speed of convergence. Moreover, we establish lower and upper bound estimates for the difference between the sequence and the Euler–Mascheroni constant.
topic	Sequences Euler–Mascheroni constant Rate of convergence Lower and upper bounds
url	http://link.springer.com/article/10.1186/s13660-018-1746-3
work_keys_str_mv	AT shanhewu anewsequencerelatedtotheeulermascheroniconstant AT gabrielbercu anewsequencerelatedtotheeulermascheroniconstant AT shanhewu newsequencerelatedtotheeulermascheroniconstant AT gabrielbercu newsequencerelatedtotheeulermascheroniconstant
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A new sequence related to the Euler–Mascheroni constant

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