Operator Bezoutiant and Roots of Entire Functions, Concrete Examples

TL;DR

This paper employs the Bezoutiant method to analyze when two entire functions, including Bessel functions, share no common roots, providing concrete examples and conditions for such cases.

Contribution

It introduces the use of the Bezoutiant method to determine root-sharing conditions for entire functions, with specific applications to Bessel functions.

Findings

Conditions for two entire functions to have no common roots

Application of the method to Bessel functions

Concrete examples illustrating the theoretical results

Abstract

In this paper we use the Bezoutiant method to describe the conditions under which two entire functions have not common roots. We apply the general results to concrete examples. In particular we consider the Bessel functions.