Fachhochschule für die Wirtschaft Hannover, Freundallee 15, 30173 Hannover, Germany
Copyright © 2009 Carsten Elsner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The author continues to study series transformations for
the Euler-Mascheroni constant . Here, we discuss in detail recently published
results of A. I. Aptekarev and T. Rivoal who found rational approximations to and () defined by linear recurrence formulae. The main purpose of
this paper is to adapt the concept of linear series transformations with integral
coefficients such that rationals are given by explicit formulae which approximate and . It is shown that for every and every integer there are infinitely many rationals for such that and with for tending to infinity.