# Iterated integrals on products of one variable multiple polylogarithms

## TL;DR

This paper proves that convergent iterated integrals of one-variable multiple polylogarithms are multiple zeta values and introduces regularized integrals for divergent cases, providing new series representations and calculations.

## Contribution

It establishes the equivalence of certain iterated integrals and multiple zeta values, including regularized cases, and offers new series representations for these values.

## Key findings

- Convergent iterated integrals equal multiple zeta values.
- Regularized integrals extend the class of multiple zeta values.
- New series representations for multiple zeta values are derived.

## Abstract

In this paper we show that the iterated integrals on products of one variable multiple polylogarithms from 0 to 1 are actually multiple zeta values if they are convergent. In the divergent case, we define regularized iterated integrals from 0 to 1. By the same method, we show that the regularized iterated integrals are also multiple zeta values. As an application, we give new series representations for multiple zeta values and calculate some interesting examples of iterated integrals.