Approximation for the gamma function via the tri-gamma function

In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are p...

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Detalles Bibliográficos
Autores principales: You, Xu, Li, Xiaocui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5732313/
https://www.ncbi.nlm.nih.gov/pubmed/29263640
http://dx.doi.org/10.1186/s13660-017-1585-7
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author You, Xu
Li, Xiaocui
author_facet You, Xu
Li, Xiaocui
author_sort You, Xu
collection PubMed
description In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.
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spelling pubmed-57323132017-12-18 Approximation for the gamma function via the tri-gamma function You, Xu Li, Xiaocui J Inequal Appl Research In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation. Springer International Publishing 2017-12-16 2017 /pmc/articles/PMC5732313/ /pubmed/29263640 http://dx.doi.org/10.1186/s13660-017-1585-7 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
You, Xu
Li, Xiaocui
Approximation for the gamma function via the tri-gamma function
title Approximation for the gamma function via the tri-gamma function
title_full Approximation for the gamma function via the tri-gamma function
title_fullStr Approximation for the gamma function via the tri-gamma function
title_full_unstemmed Approximation for the gamma function via the tri-gamma function
title_short Approximation for the gamma function via the tri-gamma function
title_sort approximation for the gamma function via the tri-gamma function
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5732313/
https://www.ncbi.nlm.nih.gov/pubmed/29263640
http://dx.doi.org/10.1186/s13660-017-1585-7
work_keys_str_mv AT youxu approximationforthegammafunctionviathetrigammafunction
AT lixiaocui approximationforthegammafunctionviathetrigammafunction

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