Inequalities for some integrals involving modified Bessel functions

TL;DR

This paper establishes tight inequalities for integrals involving modified Bessel functions, leading to new bounds for hypergeometric functions and highlighting open problems in the field.

Contribution

The paper introduces new tight inequalities for integrals with modified Bessel functions and derives bounds for hypergeometric functions, advancing mathematical analysis in special functions.

Findings

Established tight inequalities for integrals involving modified Bessel functions

Derived a tight double inequality for a generalized hypergeometric function

Presented open problems for future research in special functions

Abstract

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double inequality, involving the modified Bessel function of the first kind, for a generalized hypergeometric function. We also present some open problems that arise from this research.