A certain class of rapidly convergent series representations for ζ(2n+1)

摘要

For a natural number n, the authors propose and develop three new series representations for the Riemann Zeta function ζ(2n+1). The infinite series occurring in each of these three representations for ζ(2n+1) converges remarkably faster than that in Wilton's result. Furthermore, one of the three series representations for ζ(2n+1) involves the most rapidly convergent series among all the hitherto known members of the family of series representations considered here. Relevant connections of the results presented in this paper with many other known series representations for ζ(2n+1) are also briefly indicated.