On the calculation of two essential harmonic series with a weight 5 structure, involving harmonic numbers of the type H_2n

Abstract

. The core of the present paper is represented by the calculation of two essential har- monic series with a weight 5 structure, involving harmonic numbers of the type H 2 n . The two main series are evaluated by also exploiting results and strategies presented in the book, (Almost) Impossible Integrals, Sums, and Series , 2019.