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
Descripción
Sumario: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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