Multiple $T$-values and iterated log-tangent integrals

TL;DR

This paper explores the relationship between multiple T-values, a variant of multiple zeta values, and iterated log-tangent integrals, extending previous work on multiple zeta and log-sine integrals.

Contribution

It introduces iterated log-tangent integrals and establishes their connections with multiple T-values, advancing understanding of these special functions.

Findings

Established relations between multiple T-values and iterated log-tangent integrals

Extended previous work on multiple zeta and log-sine integrals

Provided new tools for studying level-two multiple zeta variants

Abstract

Multiple $T$-values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and discuss their relations with multiple $T$-values. We will use ideas from the author's previous work on multiple zeta values and iterated log-sine integrals to do so.