Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function

In this paper, we introduce new sequences, which generalize the celebrated DeTemple sequence, having enhanced speed of convergence. We also give a new representation for Euler’s constant in terms of the Riemann zeta function evaluated at positive odd integers.

Detalles Bibliográficos
Autores principales: Wu, Shanhe, Bercu, Gabriel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5427101/
https://www.ncbi.nlm.nih.gov/pubmed/28553060
http://dx.doi.org/10.1186/s13660-017-1385-0
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author Wu, Shanhe
Bercu, Gabriel
author_facet Wu, Shanhe
Bercu, Gabriel
author_sort Wu, Shanhe
collection PubMed
description In this paper, we introduce new sequences, which generalize the celebrated DeTemple sequence, having enhanced speed of convergence. We also give a new representation for Euler’s constant in terms of the Riemann zeta function evaluated at positive odd integers.
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spelling pubmed-54271012017-05-26 Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function Wu, Shanhe Bercu, Gabriel J Inequal Appl Research In this paper, we introduce new sequences, which generalize the celebrated DeTemple sequence, having enhanced speed of convergence. We also give a new representation for Euler’s constant in terms of the Riemann zeta function evaluated at positive odd integers. Springer International Publishing 2017-05-12 2017 /pmc/articles/PMC5427101/ /pubmed/28553060 http://dx.doi.org/10.1186/s13660-017-1385-0 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Wu, Shanhe
Bercu, Gabriel
Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
title Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
title_full Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
title_fullStr Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
title_full_unstemmed Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
title_short Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
title_sort fast convergence of generalized detemple sequences and the relation to the riemann zeta function
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5427101/
https://www.ncbi.nlm.nih.gov/pubmed/28553060
http://dx.doi.org/10.1186/s13660-017-1385-0
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