Applications of a duality between generalized trigonometric and hyperbolic functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:502

Article

Miyakawa, Hiroki¹  Takeuchi, Shingo¹ 

[1] Shibaura Inst Technol, Dept Math Sci, Minuma Ku, 307 Fukasaku, Saitama, Saitama 3378570, Japan

关键词: Generalized trigonometric functions;    Generalized hyperbolic functions;    Multiple-angle formulas;    Double-angle formulas;    p-Laplacian;   

DOI  :  10.1016/j.jmaa.2021.125241

来源: Elsevier

【 摘 要 】

It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinovic-Adamovic-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

【 授权许可】

Free