Certain families of series associated with the Hurwitz-Lerch Zeta function

The history of problems of evaluation of series associated with the Riemann Zeta function can be traced back to Christian Goldbach (1690-1764) and Leonhard Euler (1707-1783). Many different techniques to evaluate various series involving the Zeta and related functions have since then been developed. The authors show how elegantly certain families of series involving the Hurwitz-Lerch Zeta function can be evaluated by starting with a single known identity for the Hurwitz-Lerch Zeta function. Some of the special cases of these series identities are also shown to lead to certain known families of summation formulas involving the Hurwitz Zeta function.