A symmetric decomposition of the Boros-Moll polynomials

TL;DR

This paper explores a symmetric decomposition of Boros-Moll polynomials, revealing that the components are alternatingly gamma-positive, which advances understanding of their structural properties.

Contribution

It introduces a novel symmetric decomposition of Boros-Moll polynomials and demonstrates gamma-positivity in the resulting components.

Findings

Both polynomials in the symmetric decomposition are gamma-positive.

The decomposition reveals alternating gamma-positivity.

Provides new insights into the structure of Boros-Moll polynomials.

Abstract

In their study of a quartic integral, Boros and Moll introduced a special case of Jacobi polynomials, which are now known as the Boros-Moll polynomials. In this paper, we study a symmetric decomposition of Boros-Moll polynomials. We discover that both of the polynomials in the symmetric decomposition are alternatingly gamma-positive polynomials.