Multiple-angle formulas of generalized trigonometric functions with two parameters

研究成果: Article

7 引用 (Scopus)

抄録

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.

元の言語English
ページ(範囲)1000-1014
ページ数15
ジャーナルJournal of Mathematical Analysis and Applications
444
発行部数2
DOI
出版物ステータスPublished - 2016 12 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

これを引用

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abstract = "Generalized trigonometric functions with two parameters were introduced by Dr{\'a}bek and Man{\'a}sevich 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.",
keywords = "Eigenvalue problems, Generalized trigonometric functions, Lemniscate, Multiple-angle formulas, p-Laplacian, Pendulum equation",
author = "Shingo Takeuchi",
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language = "English",
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journal = "Journal of Mathematical Analysis and Applications",
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AU - Takeuchi, Shingo

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AB - 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.

KW - Eigenvalue problems

KW - Generalized trigonometric functions

KW - Lemniscate

KW - Multiple-angle formulas

KW - p-Laplacian

KW - Pendulum equation

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