Some Series of the Zeta and Related Functions

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