Windschitl type approximation formulas for the gamma function

In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and convexity. Th...

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Detalles Bibliográficos
Autores principales: Yang, Zhen-Hang, Tian, Jing-Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182422/
https://www.ncbi.nlm.nih.gov/pubmed/30363740
http://dx.doi.org/10.1186/s13660-018-1870-0
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author Yang, Zhen-Hang
Tian, Jing-Feng
author_facet Yang, Zhen-Hang
Tian, Jing-Feng
author_sort Yang, Zhen-Hang
collection PubMed
description In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and convexity. These not only yield some new inequalities for the gamma and factorial functions, but also provide a new proof of known inequalities and strengthen known results.
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spelling pubmed-61824222018-10-22 Windschitl type approximation formulas for the gamma function Yang, Zhen-Hang Tian, Jing-Feng J Inequal Appl Research In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and convexity. These not only yield some new inequalities for the gamma and factorial functions, but also provide a new proof of known inequalities and strengthen known results. Springer International Publishing 2018-10-05 2018 /pmc/articles/PMC6182422/ /pubmed/30363740 http://dx.doi.org/10.1186/s13660-018-1870-0 Text en © The Author(s) 2018 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
Tian, Jing-Feng
Windschitl type approximation formulas for the gamma function
title Windschitl type approximation formulas for the gamma function
title_full Windschitl type approximation formulas for the gamma function
title_fullStr Windschitl type approximation formulas for the gamma function
title_full_unstemmed Windschitl type approximation formulas for the gamma function
title_short Windschitl type approximation formulas for the gamma function
title_sort windschitl type approximation formulas for the gamma function
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182422/
https://www.ncbi.nlm.nih.gov/pubmed/30363740
http://dx.doi.org/10.1186/s13660-018-1870-0
work_keys_str_mv AT yangzhenhang windschitltypeapproximationformulasforthegammafunction
AT tianjingfeng windschitltypeapproximationformulasforthegammafunction

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