Two Coefficients of the Dyson Product

TL;DR

This paper derives explicit formulas for specific coefficients in the Dyson product and uncovers new Dyson-style constant term identities using an extended approach based on Good's idea.

Contribution

It provides the first closed-form expressions for the coefficients of _r^2/x_s^2 and _r^2/(_s_t) in the Dyson product, extending previous methods.

Findings

Explicit formulas for two specific Dyson product coefficients

New Dyson-style constant term identities derived

Extension of Good's idea applied successfully

Abstract

In this paper, the closed-form expressions for the coefficients of $\frac{x_r^2}{x_s^2}$ and $\frac{x_r^2}{x_sx_t}$ in the Dyson product are found by applying an extension of Good's idea. As onsequences, we find several interesting Dyson style constant term identities.