# The radius of uniform convexity of Bessel functions

## TL;DR

This paper determines the radius of uniform convexity for three normalized Bessel functions of the first kind, providing conditions for their uniform convexity within the unit disk using series expansions.

## Contribution

It introduces the exact radius of uniform convexity for three types of normalized Bessel functions and establishes conditions for their convexity in the unit disk.

## Key findings

- Normalized Bessel functions are uniformly convex within specific disks.
- Necessary and sufficient conditions for uniform convexity are provided.
- The study uses series expansions of Bessel functions as a key tool.

## Abstract

In this paper, we determine the radius of uniform convexity for three kinds of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are uniformly convex on the determined disks. Moreover, necessary and sufficient conditions are given for the parameters of the three normalized functions such that they to be uniformly convex in the open unit disk. The basic tool of this study is the development of Bessel functions in function series.