Generalized trigonometric and hyperbolic functions / Ronald E. Mickens.

Cover; Half Title; Title Page; Copyright Page; Table of Contents; Dedication; List of Figures; Preface; Author; 1: TRIGONOMETRIC AND HYPERBOLIC SINE AND COSINE FUNCTIONS; 1.1 INTRODUCTION; 1.2 SINE AND COSINE: GEOMETRIC DEFINITIONS; 1.3 SINE AND COSINE: ANALYTIC DEFINITION; 1.3.1 Derivatives; 1.3.2 Integrals; 1.3.3 Taylor Series; 1.3.4 Addition and Subtraction Rules; 1.3.5 Product Rules; 1.4 SINE AND COSINE: DYNAMIC SYSTEM APPROACH; 1.4.1 x-y Phase-Space; 1.4.2 Symmetry Properties of Trajectories in Phase-Space; 1.4.3 Null-Clines; 1.4.4 Geometric Proof that All Trajectories Are Closed

Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions. Previous efforts have started with integral representations for the inverse generalized sine functions, followed by the construction of the associated cosine functions, and from this, various properties of the generalized trigonometric functions are derived. However, the results contained in this book are based on the application of both geometrical phase space and dynamical systems methodologies. Features Clear, direct construction of a new set of generalized trigonometric and hyperbolic functions Presentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct ways All the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences

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