Shifted quadratic zeta series
Summary: It is well known that the Riemann zeta function \(\zeta \big(p\big) =\sum_{n=1}^{\infty}1/n^{p}\) can be represented in closed form for \(p\) an even integer. We define a shifted quadratic zeta series as \(\sum_{n=1}^{\infty}1/\big(4n^{2}-\alpha^{2}\big)^{p}\). In this paper, we determine closed-form representations of shifted quadratic zeta series from a recursion point of view using the Riemann zeta function. We also determine closed-form representations of alternating sign shifted quadratic zeta series.
scientific article; zbMATH DE number 2171806