TY - JOUR
T1 - Multiple-angle formulas of generalized trigonometric functions with two parameters
AU - Takeuchi, Shingo
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 24540218 .
Publisher Copyright:
© 2016 Elsevier Inc.
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 - Pendulum equation
KW - p-Laplacian
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U2 - 10.1016/j.jmaa.2016.06.074
DO - 10.1016/j.jmaa.2016.06.074
M3 - Article
AN - SCOPUS:84981510367
SN - 0022-247X
VL - 444
SP - 1000
EP - 1014
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -