Wallis序列的渐近展开式及与Glaisher-Kinkelin和Choi-Srivastava常数相关的一些新的数学常数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.2298/aadm220414024h

Xue Han, Chao-Ping Chen, H. Srivastava

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引用次数: 0

摘要

著名的沃利斯序列Wn，定义为Wn:= ?nk=1 4k2/4k2?1、已知有极限吗?2等于n ??。在不使用Bernoulli数Bn的情况下，作者给出了几个渐近展开式和确定每个渐近展开式的系数的递推关系，这些系数与Wallis序列Wn和新引入的常数D和E有关，它们类似于glaiser - kinkelin常数a和Choi-Srivastava常数B和C。

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Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants

The celebrated Wallis sequence Wn, which is defined by Wn := ?nk=1 4k2/4k2?1, is known to have the limit ? 2 as n ? ?. Without using the Bernoulli numbers Bn, the authors present several asymptotic expansions and a recurrence relation for determining the coefficients of each asymptotic expansion related to the Wallis sequence Wn and the newly-introduced constants D and E, which are analogous to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.