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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
List of contents
1 TRIGONOMETRIC AND HYPERBOLIC SINE AND CO-SINE FUNCTIONS
2 ELLIPTIC FUNCTIONS
3 SQUARE FUNCTIONS
4 PARABOLIC TRIGONOMETRIC FUNCTIONS
5 GENERALIZED PERIODIC SOLUTIONS OF f(t)2+g(t)2 = 1
6 RESUME OF (SOME) PREVIOUS RESULTS ON GENERALIZED TRIGONOMETRIC FUNCTIONS 99
7 GENERALIZED TRIGONOMETRIC FUNCTIONS: |y|p +|x|q = 1
8 GENERALIZED TRIGONOMETRIC HYPERBOLIC FUNCTIONS: |y|p − |x|q = 1
9 APPLICATIONS AND ADVANCED TOPICS
10 FINALE
About the author
Ronald E. Mickens is the Distinguished Fuller E. Callaway Professor at Clark Atlanta University, Atlanta, GA, and is a Fellow of several professional organizations, including the American Physical Society. He has written or edited seventeen books and published more than 300 peer-reviewed research articles.
Summary
The aim of this book is to highlight, to those in the area of generalized trigonometric functions, of an alternative path to the creation and analysis of these classes of functions.
