Generating functions of multiple $t$-star values of general level

Abstract: In this paper, we study the explicit expressions of multiple t-star values with an arbitrary number of blocks of twos of general level. We give an expression of a generating function of such values, which generalizes the results for multiple zeta-star values and multiple t-star values. This derived generating function can provide expressions of multiple t-star values of general level in terms of the alternating multiple t-half values of general level with additional factorial and pochhammer symbol. As applications, some specific evaluations of multiple t-star values of general level with one-two-three or more general indices are given. These evaluations contribute to a deeper understanding of the properties of multiple t-star values of general level.