Inequalities for the generalized trigonometric and hyperbolic functions
Classical Analysis and ODEs
2013-09-20 v1
Abstract
The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinovi\'c-Adamovi\'c inequality, Lazarevi\'c's inequality, Huygens-type inequalities, Wilker-type inequalities, and Cuza-Huygens-type inequalities, are generalized to the case of generalized functions.
Cite
@article{arxiv.1210.6749,
title = {Inequalities for the generalized trigonometric and hyperbolic functions},
author = {Riku Klén and Matti Vuorinen and Xiaohui Zhang},
journal= {arXiv preprint arXiv:1210.6749},
year = {2013}
}
Comments
12 pages