Multiple-angle formulas of generalized trigonometric functions with two parameters

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• 作者：Shingo Takeuchi ^{shingo@shibaura-it.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multiple-angle formulas ; Generalized trigonometric functions ; p-Laplacian ; Eigenvalue problems ; Pendulum equation ; Lemniscate
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：444
• 期：2
• 页码：1000-1014
• 全文大小：344 K

文摘

Generalized trigonometric functions with two parameters were introduced by Drábek and Manásevich 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.