Generating functions of multiple $t$-star values

TL;DR

This paper explores generating functions of multiple t-star values with various block structures, deriving explicit formulas and evaluations that extend understanding of these special mathematical sums.

Contribution

It introduces new generating functions for multiple t-star values with arbitrary blocks of twos, expanding the analytical tools available for their study.

Findings

Derived explicit expressions for multiple t-star values.

Obtained evaluations for values with complex indices.

Extended the connection between t-star values and harmonic sums.

Abstract

In this paper, we study the generating functions of multiple $t$-star values with an arbitrary number of blocks of twos, which are based on the results of the corresponding generating functions of multiple $t$-harmonic star sums. These generating functions can deduce an explicit expression of multiple $t$-star values. As applications, we obtain some evaluations of multiple $t$-star values with one-two-three or more general indices.