ASYMPTOTIC EXPANSIONS AND CONTINUED FRACTION APPROXIMATIONS FOR HARMONIC NUMBER

Applicable Analysis and Discrete Mathematics

article

Chao-Ping Chen¹  Qin Wang¹ 

[1] School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City 454000, Henan Province

关键词: Harmonic number;    Euler-Mascheroni constant;    continued fraction;    Asymptotic expansion;   

DOI  :  10.2298/AADM190111020C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In this paper, we provide a method for constructing a continued fractionapproximation based on a given asymptotic expansion. We establish someasymptotic expansions for the harmonic numbers which employ the nth triangular number. Based on these expansions, we derive the correspondingcontinued fraction approximations for the harmonic numbers.

【 授权许可】

Unknown