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

Research output: Contribution to journalArticle

8 Citations (Scopus)

### 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 language English 1000-1014 15 Journal of Mathematical Analysis and Applications 444 2 https://doi.org/10.1016/j.jmaa.2016.06.074 Published - 2016 Dec 15

### Keywords

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

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics

### Cite this

In: Journal of Mathematical Analysis and Applications, Vol. 444, No. 2, 15.12.2016, p. 1000-1014.

Research output: Contribution to journalArticle

title = "Multiple-angle formulas of generalized trigonometric functions with two parameters",
abstract = "Generalized trigonometric functions with two parameters were introduced by Dr{\'a}bek and Man{\'a}sevich 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.",
keywords = "Eigenvalue problems, Generalized trigonometric functions, Lemniscate, Multiple-angle formulas, p-Laplacian, Pendulum equation",
author = "Shingo Takeuchi",
year = "2016",
month = "12",
day = "15",
doi = "10.1016/j.jmaa.2016.06.074",
language = "English",
volume = "444",
pages = "1000--1014",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
number = "2",

}

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 -