EVALUATION OF SOME SIMPLE EULER-TYPE SERIES

Khristo N. Boyadzhiev (USA)

Received January 25, 2008

Abstract

We evaluate five series, three of which involve harmonic numbers and one involves Stirling numbers of the first kind. The evaluation of these series is reduced to the evaluation of certain integrals, including the moments of the polylogarithm.

Keywords and phrases: harmonic numbers, Stirling numbers, zeta function, polylogarithms, Euler’s Beta function.