Multiple-angle formulas of generalized trigonometric functions with two parameters

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Takeuchi, Shingo¹ 

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

关键词: Multiple-angle formulas;    Generalized trigonometric functions;    p-Laplacian;    Eigenvalue problems;    Pendulum equation;    Lemniscate;   

DOI  :  10.1016/j.jmaa.2016.06.074

来源: Elsevier

【 摘 要 】

Generalized trigonometric functions with two parameters were introduced by Drabek and Mandsevich to study an inhomogeneous eigenvalue problem of the p-Laplacian. Concerning these functions, no multiple-angle formula has been known except for the classical cases and a special case discovered by Edmunds, Gurka and Lang, not to mention addition theorems. In this paper, we will present new multiple-angle formulas which are established between two kinds of the generalized trigonometric functions, and apply the formulas to generalize classical topics related to the trigonometric functions and the lemniscate function. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free