### 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 |

巻 | 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

**Multiple-angle formulas of generalized trigonometric functions with two parameters.** / Takeuchi, Shingo.

研究成果: Article

}

TY - JOUR

T1 - Multiple-angle formulas of generalized trigonometric functions with two parameters

AU - Takeuchi, Shingo

PY - 2016/12/15

Y1 - 2016/12/15

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84981510367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981510367&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2016.06.074

DO - 10.1016/j.jmaa.2016.06.074

M3 - Article

AN - SCOPUS:84981510367

VL - 444

SP - 1000

EP - 1014

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -