# Zeros of some special entire functions

## TL;DR

This paper investigates the zeros of special entire functions like Wright, hyper-Bessel, and hypergeometric functions, extending classical theorems and addressing open problems about their zeros and derivatives.

## Contribution

It extends Hurwitz's theorem to new classes of entire functions and explores zeros of derivatives and cross-products, contributing to the understanding of their zero distributions.

## Key findings

- Extended Hurwitz's theorem to new entire functions
- Analyzed zeros of derivatives of Bessel functions
- Addressed open problems on zeros of function cross-products

## Abstract

The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel. The obtained results extend the known theorem of Hurwitz on exact number of nonreal zeros of Bessel functions of the first kind. Moreover, results on zeros of derivatives of Bessel functions and cross-product of Bessel functions are also given, which are related to some recent open problems.