Evaluation of iterated log-sine integrals in terms of multiple polylogarithms

TL;DR

This paper demonstrates how to express iterated log-sine integrals using multiple polylogarithms and zeta values, and proposes conjectures relating these special functions and constants.

Contribution

It provides explicit evaluations of iterated log-sine integrals in terms of multiple polylogarithms and zeta values, advancing the understanding of their interrelations.

Findings

Expressed iterated log-sine integrals in terms of multiple polylogarithms

Proposed conjectures on relationships among multiple zeta, Clausen, and Glaisher values

Enhanced the theoretical framework connecting special functions and constants

Abstract

It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also suggest some conjectures on multiple zeta values, multiple Clausen values, multiple Glaisher values and iterated log-sine integrals.