title: On approximating the modified Bessel function of the second kind.
abstract: 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].
authors.affiliation: School of Mathematics and Computation Sciences, Hunan City University, Yiyang, 413000 China.|Customer Service Center, State Grid Zhejiang Electric Power Research Institute, Hangzhou, 310009 China.
authors.forename: Zhen-Hang
authors.initials: ZH
authors.lastname: Yang
authors.affiliation: School of Mathematics and Computation Sciences, Hunan City University, Yiyang, 413000 China.
authors.forename: Yu-Ming
authors.initials: YM
authors.lastname: Chu
keywords: gamma function; modified Bessel function; monotonicity