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A new family of deformed trigonometric functions and their corresponding Pythagorean-like relations: application to the nonlinear harmonic oscillator

  • P. R. Gordoa
  • A. Pickering
  • D. Puertas-Centeno
  • E. V. Toranzo
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Abstract

In this work we present an extension of the classical trigonometric functions which include, amongst others, the Lindqvist p-trigonometric functions. Additionally, we show their relevance in the study of certain versions of the nonlinear harmonic oscillator equation. Furthermore, we study their more important mathematical properties and obtain their corresponding Pythagorean-like relations. We also define a new extension of the Beta and Ateb sine functions using these new χ-trigonometric functions. Indeed, these new Beta and Ateb functions are involved in the closed form expressions obtained for the solutions of the nonlinear oscillator under certain constraints.

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Cite

BibTeXRIS
BibTeX
@misc{gordoa2026family,
  title = {{A new family of deformed trigonometric functions and their corresponding Pythagorean-like relations: application to the nonlinear harmonic oscillator}},
  author = {P. R. Gordoa and A. Pickering and D. Puertas-Centeno and E. V. Toranzo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33121},
  eprint = {2610.33121},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33121},
}
RIS
TY  - UNPB
TI  - A new family of deformed trigonometric functions and their corresponding Pythagorean-like relations: application to the nonlinear harmonic oscillator
AU  - P. R. Gordoa
AU  - A. Pickering
AU  - D. Puertas-Centeno
AU  - E. V. Toranzo
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33121
UR  - https://arxiv.org/abs/2610.33121
AB  - In this work we present an extension of the classical trigonometric functions which include, amongst others, the Lindqvist p-trigonometric functions. Additionally, we show their relevance in the study of certain versions of the nonlinear harmonic oscillator equation. Furthermore, we study their more important mathematical properties and obtain their corresponding Pythagorean-like relations. We also define a new extension of the Beta and Ateb sine functions using these new χ-trigonometric functions. Indeed, these new Beta and Ateb functions are involved in the closed form expressions obtained for the solutions of the nonlinear oscillator under certain constraints.
ER  -