Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series

Abstract

We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some infinite series involving binomial coefficients. This technique can be applied to many Ap\'ery-type infinite sums.