Communications of the
Korean Mathematical Society CKMS

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

Keywords: harmonic number, Euler sum, Riemann zeta function, Stirling number

MSC numbers: 11M06, 11M32, 33B15