194 pages | 47 B/W Illus.
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.
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