Some new approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants by continued fraction

JOURNAL OF NUMBER THEORY

卷:163

Article

Lu, Dawei¹  Mortici, Cristinel²  Song, Lixin¹ 

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116023, Peoples R China

[2] Valahia Univ Targoviste, Dept Math, Bd Unirii 18, Targoviste 130082, Romania

关键词: Glaisher-Kinkelin's constant;    Bendersky-Adamchik's constants;    Rate of convergence;    Asymptotic expansion;   

DOI  :  10.1016/j.jnt.2015.12.008

来源: Elsevier

【 摘 要 】

In this paper, some new continued fraction approximations, inequalities and rates of convergence of Glaisher-Kinkelin's and Bendersky-Adamchik's constants are provided. Finally, for demonstrating the superiority of our new convergent sequences over the classical sequences and Mortici's sequences, some numerical computations are also given. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free