Extension of Frame's type inequalities to Bessel and modified Bessel functions

TL;DR

This paper extends classical trigonometric inequalities to Bessel and modified Bessel functions, generalizing Cusa-type inequalities and providing new bounds, motivated by recent related research.

Contribution

It introduces novel inequalities for Bessel functions, extending existing trigonometric bounds and their hyperbolic analogues, enriching the mathematical theory of special functions.

Findings

Generalized Cusa-type inequality for modified Bessel functions

Extended trigonometric inequalities to Bessel functions

Provided new bounds and inequalities for special functions

Abstract

Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we extend the hyperbolic analogue of these trigonometric inequalities. As an application of these results we present a generalization of Cusa-type inequality to modified Bessel function. Our main motivation to write this paper is a recent publication of Chen and S\'andor, which we wish to complement.