Generalized Trigonometric and Hyperbolic Functions

By: Ronald E. Mickens

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Hardcover | 14 January 2019 | Edition Number 1

At a Glance

Hardcover
214 Pages

Dimensions(cm)
23.4 x 15.6 x 1.91

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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.

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

Industry Reviews

"Differing from the standard approach, this book argues the benefits of creating and analyzing generalized trigonometric functions using methodologies involving geometrical phase-space and dynamical systems. This is a mouthful, but Mickens (Clark Atlanta Univ.) takes on his subject with vigor. After a brief overview of the standard approaches and results, Mickens discusses square and parabolic forms of periodic and hyperbolic functions, as well as their generalized forms. From this basic understanding, he uses special functional equations to define a 'new class' of generalized trigonometric and hyperbolic functions, which he uses to model important dynamical systems."

-J. Johnson, Emeritus Professor, Western Washington University

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