探索三角函数和双曲函数的显式定积分公式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-31 DOI:10.3390/axioms13040230

Yulei Chen, Dongwei Guo

引用次数: 0

摘要

利用分式积分法和变量置换法，我们推导出一些涉及三角函数或双曲函数的有趣的显式定积分公式，其结果用卡塔兰常数、狄里克特贝塔函数和黎曼zeta函数以及分母中的π表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exploring Explicit Definite Integral Formulae with Trigonometric and Hyperbolic Functions

Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan’s constant, Dirichlet’s beta function, and Riemann’s zeta function, as well as π in the denominator.

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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.