Generalized trigonometric and hyperbolic functions
著者
書誌事項
Generalized trigonometric and hyperbolic functions
CRC Press, c2019
- : hardback
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注記
"A Chapman & Hall book"--Cover
Includes bibliographical references and index
内容説明・目次
内容説明
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
目次
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
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