用欧拉和求log - tan积分

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-02-07 DOI:10.3846/mma.2022.13100

A. Sofo

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引用次数: 3

摘要

本文将研究对数函数与arctan函数乘积的积分的表示，并将其简化为log-tan积分。我们会证明，在很多情况下，这些积分都是显式的，包括黎曼函数，狄利克雷函数，狄利克雷函数和许多其他的特殊函数。下面将详细地举例说明这些定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Evaluating Log-Tangent integrals via Euler sums

An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.

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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.