Shifted quadratic Zeta series

It is well known that the Riemann Zeta function ς(p)=∑n=1∞1/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑n=1∞1/(4n2−α2)p. In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will alsodetermine closed-form representations of alternating sign shifted quadratic Zeta series