Evaluation of some simple Euler-type series

Abstract

Five series are evaluated in terms of zeta values. Three of the series 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.

References in corpus (1)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I

Cited by in corpus (1)

• Logarithmic Integrals, Polylogarithmic Integrals and Euler sums