TY - JOUR

T1 - Applications of generalized trigonometric functions with two parameters

AU - Kobayashi, Hiroyuki

AU - Takeuchi, Shingo

N1 - Funding Information:
2000 Mathematics Subject Classification. Primary: 33B10, 34B10. Key words and phrases. Generalized trigonometric functions, p-Laplacian, Gaussian hyperge- ometric functions, Wallis-type formulas. The work of S. Takeuchi was supported by JSPS KAKENHI Grant Number 17K05336. ∗ Corresponding author.
Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.

PY - 2019/5

Y1 - 2019/5

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

AN - SCOPUS:85056482954

SN - 1534-0392

VL - 18

SP - 1509

EP - 1521

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 3

ER -