Applications of a duality between generalized trigonometric and hyperbolic functions II
Copyright policy )Applications of a duality between generalized trigonometric and hyperbolic functions II
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.
15pages, 2 figures, 1 table
multiple-angle formula, Trigonometric solutions to PDEs, p-Laplacian, Huygens inequality, Cusa-Huygens inequality, Nonlinear ordinary differential equations and systems, generalized trigonometric function, Wilker inequality, \(p\)-Laplacian, generalized hyperbolic function, Exponential and trigonometric functions, Mathematics - Analysis of PDEs, Mitrinović-Adamović inequality, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inequalities for trigonometric functions and polynomials, double-angle formula, Inequalities involving other types of functions, Other generalizations (nonlinear potential theory, etc.), Analysis of PDEs (math.AP)
multiple-angle formula, Trigonometric solutions to PDEs, p-Laplacian, Huygens inequality, Cusa-Huygens inequality, Nonlinear ordinary differential equations and systems, generalized trigonometric function, Wilker inequality, \(p\)-Laplacian, generalized hyperbolic function, Exponential and trigonometric functions, Mathematics - Analysis of PDEs, Mitrinović-Adamović inequality, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inequalities for trigonometric functions and polynomials, double-angle formula, Inequalities involving other types of functions, Other generalizations (nonlinear potential theory, etc.), Analysis of PDEs (math.AP)
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