Integrals of polylogarithms and infinite series involving generalized harmonic numbers

Abstract

In this paper, we give an explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers in terms of polylogarithm functions. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.

Keywords:

• Polylogarithm function
• integration by parts
• generalized harmonic numbers

2020 MR Subject Classifications:

• 40A25
• 33E20
• 11B83

Acknowledgements

The author is grateful to the referee for her/his useful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).