### 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 language | English |
---|---|

Pages (from-to) | 1509-1521 |

Number of pages | 13 |

Journal | Communications on Pure and Applied Analysis |

Volume | 18 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2019 May 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Analysis*,

*18*(3), 1509-1521. https://doi.org/10.3934/cpaa.2019072

**Applications of generalized trigonometric functions with two parameters.** / Kobayashi, Hiroyuki; Takeuchi, Shingo.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Analysis*, vol. 18, no. 3, pp. 1509-1521. https://doi.org/10.3934/cpaa.2019072

}

TY - JOUR

T1 - Applications of generalized trigonometric functions with two parameters

AU - Kobayashi, Hiroyuki

AU - Takeuchi, Shingo

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - Gaussian hypergeometric functions

KW - Generalized trigonometric functions

KW - P-Laplacian

KW - Wallis-type formulas

UR - http://www.scopus.com/inward/record.url?scp=85056482954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056482954&partnerID=8YFLogxK

U2 - 10.3934/cpaa.2019072

DO - 10.3934/cpaa.2019072

M3 - Article

VL - 18

SP - 1509

EP - 1521

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

SN - 1534-0392

IS - 3

ER -