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Braun, J.; Romberger, D.; Bentz, H. J. (2017): Fast converging series for zeta numbers in terms of polynomial representations of Bernoulli numbers. In: Notes On Number theory and Discrete Mathematics, Vol. 23, No. 2: pp. 54-80
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Abstract

In this paper we introduce a new polynomial representation of the Bernoulli numbers in terms of polynomial sums allowing on the one hand a more detailed understanding of their mathematical structure and on the other hand provides a computation of B-2n as a function of B2n-2 only. Furthermore, we show that a direct computation of the Riemann zeta-function and their derivatives at k is an element of Z is possible in terms of these polynomial representation. As an explicit example, our polynomial Bernoulli number representation is applied to fast approximate computations of zeta (3);zeta (5) and zeta (7).