The radius of convexity of normalized Bessel functions

TL;DR

This paper determines the radius of convexity for two normalized Bessel functions of the first kind with orders between -2 and -1, using advanced complex analysis techniques.

Contribution

It introduces new methods to compute the radius of convexity for specific Bessel functions based on harmonic functions and zero properties.

Findings

Radius of convexity determined for the specified Bessel functions

Methods involve harmonic functions and Hadamard factorization

Results extend understanding of Bessel function convexity properties

Abstract

The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of some Dini functions, properties of the zeros of Dini functions via Lommel polynomials and some inequalities for complex and real numbers.