On approximating the modified Bessel function of the second kind

In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text] , where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bou...

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Detalles Bibliográficos
Autores principales: Yang, Zhen-Hang, Chu, Yu-Ming
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5306441/
https://www.ncbi.nlm.nih.gov/pubmed/28250694
http://dx.doi.org/10.1186/s13660-017-1317-z
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author Yang, Zhen-Hang
Chu, Yu-Ming
author_facet Yang, Zhen-Hang
Chu, Yu-Ming
author_sort Yang, Zhen-Hang
collection PubMed
description In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text] , where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bounds for [Formula: see text] with [Formula: see text] and present the necessary and sufficient condition such that the function [Formula: see text] is strictly increasing (decreasing) on [Formula: see text] .
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spelling pubmed-53064412017-02-27 On approximating the modified Bessel function of the second kind Yang, Zhen-Hang Chu, Yu-Ming J Inequal Appl Research In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text] , where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bounds for [Formula: see text] with [Formula: see text] and present the necessary and sufficient condition such that the function [Formula: see text] is strictly increasing (decreasing) on [Formula: see text] . Springer International Publishing 2017-02-13 2017 /pmc/articles/PMC5306441/ /pubmed/28250694 http://dx.doi.org/10.1186/s13660-017-1317-z 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
Chu, Yu-Ming
On approximating the modified Bessel function of the second kind
title On approximating the modified Bessel function of the second kind
title_full On approximating the modified Bessel function of the second kind
title_fullStr On approximating the modified Bessel function of the second kind
title_full_unstemmed On approximating the modified Bessel function of the second kind
title_short On approximating the modified Bessel function of the second kind
title_sort on approximating the modified bessel function of the second kind
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5306441/
https://www.ncbi.nlm.nih.gov/pubmed/28250694
http://dx.doi.org/10.1186/s13660-017-1317-z
work_keys_str_mv AT yangzhenhang onapproximatingthemodifiedbesselfunctionofthesecondkind
AT chuyuming onapproximatingthemodifiedbesselfunctionofthesecondkind

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