Harmonic series with polylogarithmic functions

Abstract

Introduction/purpose: Some sums of the polylogarithmic function associated with harmonic numbers are established. Methods: The approach is based on using the summation methods. Results: This paper generalizes the results of the zeta function series associated with the harmonic numbers. Conclusions: Various interesting series as the consequence of the generalization are obtained.

Keywords

• polylogarithmic function
• series
• harmonic numbers
• integration