Complete monotonicity involving some ratios of gamma functions

In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certa...

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Detalles Bibliográficos
Autores principales: Yang, Zhen-Hang, Zheng, Shen-Zhou
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5636920/
https://www.ncbi.nlm.nih.gov/pubmed/29081631
http://dx.doi.org/10.1186/s13660-017-1527-4
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author Yang, Zhen-Hang
Zheng, Shen-Zhou
author_facet Yang, Zhen-Hang
Zheng, Shen-Zhou
author_sort Yang, Zhen-Hang
collection PubMed
description In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certain known results including Qi’s and Ismail’s conclusions, but also can generate some new inequalities.
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spelling pubmed-56369202017-10-25 Complete monotonicity involving some ratios of gamma functions Yang, Zhen-Hang Zheng, Shen-Zhou J Inequal Appl Research In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certain known results including Qi’s and Ismail’s conclusions, but also can generate some new inequalities. Springer International Publishing 2017-10-11 2017 /pmc/articles/PMC5636920/ /pubmed/29081631 http://dx.doi.org/10.1186/s13660-017-1527-4 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
Yang, Zhen-Hang
Zheng, Shen-Zhou
Complete monotonicity involving some ratios of gamma functions
title Complete monotonicity involving some ratios of gamma functions
title_full Complete monotonicity involving some ratios of gamma functions
title_fullStr Complete monotonicity involving some ratios of gamma functions
title_full_unstemmed Complete monotonicity involving some ratios of gamma functions
title_short Complete monotonicity involving some ratios of gamma functions
title_sort complete monotonicity involving some ratios of gamma functions
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5636920/
https://www.ncbi.nlm.nih.gov/pubmed/29081631
http://dx.doi.org/10.1186/s13660-017-1527-4
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AT zhengshenzhou completemonotonicityinvolvingsomeratiosofgammafunctions

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