Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials

TL;DR

This paper proves a strong conjecture regarding the coefficients of the exponential of a polynomial, utilizing properties of Gould-Hopper polynomials, thereby confirming a related weaker conjecture.

Contribution

The paper introduces a proof of the strong conjecture on exponential polynomial coefficients using Gould-Hopper polynomial properties, advancing understanding in this mathematical area.

Findings

Proof of the strong conjecture confirmed

Weak conjecture is a special case of the strong one

Method relies on properties of Gould-Hopper polynomials

Abstract

We prove the "strong conjecture" expressed by Gazeau et al. in arXiv:1203.3936v1 [math-ph] about the coefficients of the Taylor expansion of the exponential of a polynomial. This implies the "weak conjecture" as a special case. The proof relies mainly about properties of the Gould-Hopper polynomials.