# Inequalities for the modified Bessel function of the second kind and the kernel of the Kr\"{a}tzel integral transformation

## TL;DR

This paper derives new inequalities for the modified Bessel function of the second kind by establishing bounds for the kernel of the Krätzel integral transformation, connecting special functions and integral transforms.

## Contribution

It introduces novel inequalities for $K_
u$ based on the Krätzel kernel, expanding the understanding of these functions and their bounds.

## Key findings

- New inequalities for $K_
u$ in terms of gamma functions
- Bounds derived for the Krätzel integral transformation kernel
- Special cases recover known inequalities

## Abstract

We obtain new inequalities for the modified Bessel function of the second kind $K_\nu$ in terms of the gamma function. These bounds follow as special cases of inequalities that we derive for the kernel of the Kr\"{a}tzel integral transformation.