Generalized rational zeta series for $\zeta (2n)$ and $\zeta (2n+1)$

Derek Orr

In this paper, we find rational zeta series with $\zeta (2n)$ in terms of $\zeta (2k+1)$ and $\beta (2k)$, the Dirichlet beta function. We then develop a certain family of generalized rational ze…