Generating functions for multiple zeta star values

TL;DR

This paper explores generating functions for multiple zeta star values, establishing connections with Euler sums and enabling the expression of these values in terms of alternating sums, with a focus on simplifying the structure of the sums.

Contribution

It introduces a general form of generating functions for multiple zeta star values and links them to multiple Euler sums, reducing complexity in the resulting sums.

Findings

Expressed multiple zeta star values using Euler sums

Reduced the length of blocks of twos in sums

Established a connection between zeta star values and Euler sums

Abstract

We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value in terms of multiple alternating Euler sums, and specifically, reduce the length of blocks of twos in the resulting sums.