Applications of a duality between generalized trigonometric and hyperbolic functions II

Abstract

Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple- and double-angle formulas not previously obtained are also given.

arXiv comment15pages, 2 figures, 1 table

References in corpus (3)

• Multiple-angle formulas of generalized trigonometric functions with two parameters
• Two double-angle formulas of generalized trigonometric functions
• Addition Formulas of Leaf Functions According to Integral Root of Polynomial Based on Analogies of Inverse Trigonometric Functions and Inverse Lemniscate Functions

Cited by in corpus (2)

• Generalized and new solutions of the NRT nonlinear Schrödinger equation
• A look at generalized trigonometric functions as functions of their two parameters and further new properties