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We construct sequences of finite sums (l˜n)n≥0$(\tilde{l}_{n})_{n\geq 0}$ and (u˜n)n≥0$(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy… Click to show full abstract
We construct sequences of finite sums (l˜n)n≥0$(\tilde{l}_{n})_{n\geq 0}$ and (u˜n)n≥0$(\tilde{u}_{n})_{n\geq 0}$ 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 2γ$2^{\gamma }$ 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.
Journal Title: Journal of Inequalities and Applications
Year Published: 2017
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