Abstract. For a natural number n, the author derives several families of series representations for the Riemann Zeta function ζ(2n + 1). Each of these series representing ζ(2n + 1) converges remarkably rapidly with its general term having the order estimate: O(k −2n−1 · m −2k) (k →∞; m=2,3,4,6). Relevant connections of the results presented here with many other known series representations for ζ(2n +1)arealsopointedout. 1. Introduction an
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