Type: Article
Publication Date: 2017-09-15
Citations: 0
DOI: https://doi.org/10.1186/s13660-017-1507-8
We construct sequences of finite sums $(\tilde{l}_{n})_{n\geq 0}$ and $(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ 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 $2^{\gamma }$ 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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