On Rational Approximations to Euler's Constant and to

Abstract

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.