Inequalities for integrals of modified Bessel functions and expressions involving them

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:462

Article

Gaunt, Robert E.¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Modified Bessel function;    Inequality;    Integral;   

DOI  :  10.1016/j.jmaa.2018.02.003

来源: Elsevier

【 摘 要 】

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We apply these inequalities to obtain uniform bounds for several expressions involving integrals of modified Bessel functions. Such expressions occur in Stein's method for variance gamma approximation, and the results obtained in this paper allow for technical advances in the method. We also present some open problems that arise from this research. (C) 2018 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license.

【 授权许可】

Free