Some explicit values of a $q$-multiple zeta-star function at roots of unity

TL;DR

This paper derives explicit formulas for certain $q$-multiple zeta-star values at roots of unity using determinants, Bell polynomials, and recurrence relations from generating functions, advancing understanding of these special functions.

Contribution

The paper provides new explicit formulas for $q$-multiple zeta-star values at roots of unity, connecting them with determinants, Bell polynomials, and recurrence relations.

Findings

Explicit formulas expressed via determinants and Bell polynomials.

Recurrence relations derived from generating functions.

Extensions to other value types through recurrence relations.

Abstract

In this paper, we show some expressions of certain $q$-multiple zeta-star values at roots of unity. These explicit formulas are expressed by using the determinants or Bell polynomials. Explicit formulas for other types of values can be found from recurrence relations obtained using generating functions.