Fast converging series for zeta numbers in terms of polynomial representations of Bernoulli numbers

Content Provider	Semantic Scholar
Author	Braun, Jean Romberger, Dj Bentz, H. J.
Copyright Year	2015
Abstract	In this work 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 B$_{2n-2}$ only. Furthermore, we show that a direct computation of the Riemann zeta-function and their derivatives at k $\in \mathbb Z$ 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).
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://arxiv.org/pdf/1503.04636v2.pdf
Alternate Webpage(s)	http://nntdm.net/papers/nntdm-23/NNTDM-23-2-054-080.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article