Identity involving symmetric sums of regularized multiple zeta-star values

TL;DR

This paper proves a new shuffle-type identity involving symmetric sums of regularized multiple zeta-star values, expanding the mathematical understanding of these special functions.

Contribution

It introduces a novel shuffle-type identity for regularized multiple zeta-star values using Bell polynomials, complementing Hoffman's harmonic-type identity.

Findings

Established a shuffle-type identity for regularized multiple zeta-star values

Utilized Bell polynomials to prove the identity

Extended the theoretical framework of multiple zeta values

Abstract

An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to prove the identity.