We propose and develop yet another approach to the problem of summation of series involving the Riemann zeta-function
, the (Hurwitz’s) generalized zeta-function
, the Polygamma function
and the polylogarithmic function
. The key ingredients in our approach include certain known integral representations for
. The method in this paper is illustrated by numerous examples of closed-form evaluations of series of the aforementioned types; the method developed in Section 2, in particular, has been implemented in Mathematica (Version 3.0). Many of the resulting summation formulas are believed to be new.