Shifted quadratic Zeta series

It is well known that the Riemann Zeta function ζ ( 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 also determine closed-form representations of alternating sign shifted quadratic Zeta series.