Ronald E. Mickens Generalized Trigonometric and Hyperbolic Functions

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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.FeaturesClear, direct construction of a new set of generalized trigonometric and hyperbolic functionsPresentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct waysAll the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences