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

Braun, J.; Romberger, D. und 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, Bd. 23, Nr. 2: S. 54-80

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).

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Chemie und Pharmazie > Department Chemie
• Themengebiete: 500 Naturwissenschaften und Mathematik > 540 Chemie
• ISSN: 1310-5132
• Sprache: Englisch