APPLICATIONS OF A DUALITY BETWEEN GENERALIZED TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS II

被引：5

作者：

Miyakawa, Hiroki ^{[1
]}

Takeuchi, Shingo ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2022年 / 16卷 / 04期

关键词：

Generalized trigonometric function; Generalized hyperbolic function; Mitri-novi?-Adamovi? inequality; Wilker inequality; Huygens inequality; Cusa-Huygens inequality; Multiple-angle formula; Double-angle formula; p-Laplacian; INEQUALITIES;

D O I：

10.7153/jmi-2022-16-102

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Generalized trigonometric functions and generalized hyperbolic functions can be con-verted 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 ad-dition, multiple-and double-angle formulas not previously obtained are also given.

引用

页码：1571 / 1585

页数：15

共 15 条

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SHINOHARA KAZUNORI, 2017, APPL MATH SCI, V11, P2561

[12] Some double-angle formulas related to a generalized lemniscate function [J].