Abstract
We study a problem of finding good approximations to Euler's constant = limn!1 Sn, where Sn = P n=1 1 − log(n + 1), by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence Sn can be significantly improved if Sn is replaced by linear combinations of Sn with integer coefficients. In this paper, considering more general linear transformations of the sequence Sn we establish new accelerating convergence formulae for . Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results.
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