Some classes of infinite series associated with the Riemann Zeta and Polygamma functions and generalized harmonic numbers

Abstract

The authors aim at presenting a systematic investigation of several families of infinite series which are associated with the Riemann Zeta function, the Digamma (and Polygamma) functions, the harmonic (and generalized harmonic) numbers, and the Stirling numbers of the first kind. Relevant connections of the results derived here with those considered in many earlier works on this subject are also indicated.