  We evaluate in closed form three special classes of alternating zeta series
with one and two additional parameters. Two classes are expressed as linear
combinations of polylogarithms while for the third class we prove an expression
involving the incomplete gamma function and the exponential integral. We also
present some related series that can be deduced from the main results as well
as some series with Fibonacci and Lucas numbers as coefficients. Particular
cases of the series presented here will be rediscoveries of identities
established by Zhang and Williams, Choi and Srivastava, and Orr, among others.
We will also rediscover a series identity published by Mez\H{o} in 2015 as a
problem proposal in the American Mathematical Monthly.
