广义三角函数与双曲函数对偶的应用II

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-03-13 DOI:10.7153/jmi-2022-16-102

Hiroki Miyakawa, S. Takeuchi

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引用次数: 4

摘要

广义三角函数和广义双曲函数可以用作者先前发现的对偶公式相互转换。本文应用对偶公式证明了广义函数的wilker型不等式、huygens型不等式和(松弛的)cusa - huygens型不等式的对偶对。此外，还给出了先前未得到的多角和双角公式。

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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Applications of a duality between generalized trigonometric and hyperbolic functions II

Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple- and double-angle formulas not previously obtained are also given.

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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.

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