Monotone and fast computation of Euler’s constant

We construct sequences of finite sums [Formula: see text] and [Formula: see text] converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequen...

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Detalles Bibliográficos
Autores principales: Adell, José A, Lekuona, Alberto
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5602063/
https://www.ncbi.nlm.nih.gov/pubmed/28983179
http://dx.doi.org/10.1186/s13660-017-1507-8
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author Adell, José A
Lekuona, Alberto
author_facet Adell, José A
Lekuona, Alberto
author_sort Adell, José A
collection PubMed
description We construct sequences of finite sums [Formula: see text] and [Formula: see text] converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for [Formula: see text] converging in a monotone and fast way at the same time. We use a probabilistic approach based on a differentiation formula for the gamma process.
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spelling pubmed-56020632017-10-03 Monotone and fast computation of Euler’s constant Adell, José A Lekuona, Alberto J Inequal Appl Research We construct sequences of finite sums [Formula: see text] and [Formula: see text] converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for [Formula: see text] converging in a monotone and fast way at the same time. We use a probabilistic approach based on a differentiation formula for the gamma process. Springer International Publishing 2017-09-15 2017 /pmc/articles/PMC5602063/ /pubmed/28983179 http://dx.doi.org/10.1186/s13660-017-1507-8 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
Adell, José A
Lekuona, Alberto
Monotone and fast computation of Euler’s constant
title Monotone and fast computation of Euler’s constant
title_full Monotone and fast computation of Euler’s constant
title_fullStr Monotone and fast computation of Euler’s constant
title_full_unstemmed Monotone and fast computation of Euler’s constant
title_short Monotone and fast computation of Euler’s constant
title_sort monotone and fast computation of euler’s constant
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5602063/
https://www.ncbi.nlm.nih.gov/pubmed/28983179
http://dx.doi.org/10.1186/s13660-017-1507-8
work_keys_str_mv AT adelljosea monotoneandfastcomputationofeulersconstant
AT lekuonaalberto monotoneandfastcomputationofeulersconstant

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