Monotone and fast computation of Euler’s constant

Journal of Inequalities and Applications

卷:2017

Alberto Lekuona¹  José A Adell¹ 

[1] Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza;

关键词: Euler-Mascheroni constant;    fast computation;    infinite product;    alternating zeta function;    gamma process;   

DOI  :  10.1186/s13660-017-1507-8

来源: DOAJ

【 摘 要 】

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 2 γ $2^{\gamma }$ 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.

【 授权许可】

Unknown