We construct sequences of finite sums [Formula: see text] and [Formula: see text] converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for [Formula: see text] converging in a monotone and fast way at the same time. We use a probabilistic approach based on a differentiation formula for the gamma process.
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| http://dx.doi.org/10.1186/s13660-017-1507-8 | DOI Listing |
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