Multiple-angle formulas of generalized trigonometric functions with two parameters

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Abstract

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.

Original languageEnglish
Pages (from-to)1000-1014
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume444
Issue number2
DOIs
Publication statusPublished - 2016 Dec 15

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Keywords

  • Eigenvalue problems
  • Generalized trigonometric functions
  • Lemniscate
  • Multiple-angle formulas
  • p-Laplacian
  • Pendulum equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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