Further series representations for ζ(2n + 1)

摘要

For a natural number n, we propose and develop yet another family of rapidly converging series representations for the Riemann Zeta function ζ(2n + 1). These developments lead us naturally to the problem of computation of the derivatives ζ′(1 − 2n) and ζ′(−n, a) of the Riemann and Hurwitz Zeta functions, respectively. We also briefly indicate relevant connections of the results considered here with many other known series representations for ζ(2n + 1).