Positivity of the Rational Function of Gillis, Reznick and Zeilberger

TL;DR

This paper proves that a specific rational function introduced by Gillis, Reznick, and Zeilberger in 1983 has a power series expansion with exclusively nonnegative coefficients, confirming a positivity property.

Contribution

It establishes the positivity of the power series coefficients for the Gillis-Reznick-Zeilberger rational function, a result not previously proven.

Findings

Power series expansion has only nonnegative coefficients.

Confirms a conjecture about the positivity of this rational function.

Provides a rigorous proof of the positivity property.

Abstract

We prove that the power series expansion of the rational function of Gillis, Reznick and Zeilberger (1983) has only nonnegative coefficients.