一些关于常数e和函数(1+1/x)x的新结果

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI:10.2298/aadm230219019h

Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava

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引用次数: 0

摘要

已知常数e有以下级数表示:e = ??k = 0 1 / k !e = ??k = 0 9 k2 + 1 / (3 k) !。第二个级数的收敛速度非常快。本文给出了余数Rn和Rn的渐近展开式和双边不等式，其中Rn = e ?n k=0 1/k!和Rn = e ? ?N k= 9k2+1/(3k)!同时，我们也给出了涉及(1 + 1/x)x的一些不等式和完全单调函数。我们还审议了关于本文主题的若干相关发展。

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Some new results related to the constant e and function (1+1/x)x

It is known that the constant e has the following series representations: e = ?? k=0 1/k! and e = ?? k=0 9k2+1/(3k)!. The second series is extremely rapidly convergent. In this paper, we present asymptotic expansions and two-sided inequalities for the remainders Rn and Rn, where Rn = e ? ?n k=0 1/k! and Rn=e??n k=0 9k2+1/(3k)!. Also, we present some inequalities and completely monotonic functions involving (1 + 1/x)x. We also consider a number of related developments on the subject of this paper.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).