Applications of generalized trigonometric functions with two parameters

Hiroyuki Kobayashi, Shingo Takeuchi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the p-Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of works on GTFs concerning the p-Laplacian. However, few applications to differential equations unrelated to the p-Laplacian are known. We will apply GTFs with two parameters to nonlinear nonlocal boundary value problems without p-Laplacian. Moreover, we will give integral formulas for the functions, e.g. Wallis-type formulas, and apply the formulas to the lemniscate function and the lemniscate constant.

Original languageEnglish
Pages (from-to)1509-1521
Number of pages13
JournalCommunications on Pure and Applied Analysis
Volume18
Issue number3
DOIs
Publication statusPublished - 2019 May

Keywords

  • Gaussian hypergeometric functions
  • Generalized trigonometric functions
  • P-Laplacian
  • Wallis-type formulas

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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