Closed-form expressions for polylogarithmic integrals and related harmonic sums

Abstract

 This paper derives closed-form expressions for a class of five-parameter polylogarithmic integrals, expressed in terms of the polylogarithm and Lerch transcendent, and reducible (under admissible parameter choices) to Riemann and Hurwitz zeta values. The paper further obtains closed forms for related linear Euler-type sums and BBP-type series. All results are established using purely real-analytic methods.