TY - JOUR
T1 - Applications of a duality between generalized trigonometric and hyperbolic functions
AU - Miyakawa, Hiroki
AU - Takeuchi, Shingo
N1 - Funding Information:
The work of S.T. was supported by JSPS KAKENHI Grant Number 17K05336 .
Publisher Copyright:
© 2021 The Author(s)
PY - 2021/10/1
Y1 - 2021/10/1
N2 - It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinović-Adamović-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced.
AB - It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinović-Adamović-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced.
KW - Double-angle formulas
KW - Generalized hyperbolic functions
KW - Generalized trigonometric functions
KW - Multiple-angle formulas
KW - p-Laplacian
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U2 - 10.1016/j.jmaa.2021.125241
DO - 10.1016/j.jmaa.2021.125241
M3 - Article
AN - SCOPUS:85104467797
SN - 0022-247X
VL - 502
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 125241
ER -