Bounds for an integral of the modified Bessel function of the first kind and expressions involving it

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:502

Article

Gaunt, Robert E.¹ 

[1] Univ Manchester, Dept Math, Oxford Rd, Manchester M13 9PL, Lancs, England

关键词: Modified Bessel function;    Inequality;    Integral;   

DOI  :  10.1016/j.jmaa.2021.125216

来源: Elsevier

【 摘 要 】

Simple upper and lower bounds are obtained for the integral integral(x)(0) e(-gamma)tt(v)I(v)(t)dt, x > 0, nu >-1/2 , 0 < gamma < 1. Most of our bounds for this integral are tight as x -> infinity. We apply one of our inequalities to bound some expressions involving this integral. Two of these expressions appear in Stein's method for variance-gamma approximation, and our bounds will allow for a technical advancement to be made to the method. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free