收敛到Euler-Mascheroni常数的改进序列

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大键词：Euler-Vascheroni常数;收敛序列；收敛速度;渐近展开；快速计昇中图分类号：0174.6 文献标志码：A 文章编号：1673-3851（2025）11-0872-11引文格式：，．收敛到Euler-Mascheroni常数的改进序列[J]．浙江理工大学学报（自然科学），2025，53（6）：872-882.Reference Format： YU Hang，ZHANG Xiaohui.Modified sequences convergent to the Euler-Mascheroni constant[J].Journal of Zhejiang Sci-Tech University，2025，53（6）：872-882.

Modified sequences convergent to the Euler-Mascheroni constant

YU Hang， ZHANG Xiaohui （School of Science，Zhejiang Sci-Tech University，Hangzhou 31Oo18，China）

Abstract： The rapid approximation of the Euler-Mascheroni constant （Euler constant） has been of interest to researchers in recent years. To compute the Euler constant quickly，we studied the problem that some sequences converged quickly to the Euler constant and related inequalities. By modifying the term in the harmonic sum of Euler sequence and introducing the continued fraction to the logarithm term， we presented two new sequences convergent to the Euler constant based on the above modifications and proved the convergence speed of them， then obtained and compared the approximate value of some sequences by numerical computations. The results show that the established approximation inequalities for the Euler constant based on the new sequences extend and improve some related previous known approximation inequalities. Numerical computations demonstrate the new sequences can converge more quickly to the Euler constant. The obtained modified sequences are of significance in the rapid computation of the Euler constant.

Key Words： Euler-Mascheroni constant； convergent sequence; convergence speed; asymptotic expansion; rapid computation

0引言

Euler-Mascheroni常数（或简称Euler常数） γ=0.577215… ·由如下极限定义：

其中：序列 （γn）n⩾1 称为Euler序列。（剩余7739字）