A new identity linking coefficients of a certain class of homogeneous polynomials and Gauss hypergeometric functions

TL;DR

This paper presents a novel identity linking coefficients of specific homogeneous polynomials with Gauss hypergeometric functions, supported by a direct proof, indicating potential for deeper mathematical insights.

Contribution

It introduces a new identity involving polynomial coefficients and hypergeometric functions, with a direct proof and implications for further research.

Findings

Discovered a new identity involving polynomial coefficients and hypergeometric functions

Provided a direct proof of the identity

Suggests deeper underlying mathematical structures

Abstract

In investigating the properties of a certain class of homogeneous polynomials, we discovered an identity satisfied by their coefficients which involves simple 2F1 Gauss hypergeometric functions. This result appears to be new and we supply a direct proof. The simplicity of the identity is suggestive of a deeper result.