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 Apéry-type infinite sums.

References in corpus (3)

• Multiple polylogarithm values at roots of unity
• On logarithmic integrals, harmonic sums and variations
• Linear relations between logarithmic integrals of high weight and some closed-form evaluations

Cited by in corpus (2)

• Explicit Relations between Kaneko--Yamamoto Type Multiple Zeta Values and Related Variants
• MZV evaluation of hypergeometric series