Generalized Trigonometric and Hyperbolic Functions

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.

• 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 997 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

"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