Hyperbolic Functions

João Pedro Morais, Svetlin Georgiev and Wolfgang Sprößig
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João Pedro Morais: University of Aveiro, CIDMA
Svetlin Georgiev: University of Sofia St Kliment Ohridski Faculty of Mathematics and Informatics, Department of Differential Equations
Wolfgang Sprößig: TU Bergakademie Freiberg, Institut für Angewandte Analysis

Chapter 7 in Real Quaternionic Calculus Handbook, 2014, pp 117-124 from Springer

Abstract: Abstract After bringing together various results mentioned before, in this chapter we introduce the quaternion hyperbolic functions, whose study will require us to master a new situation. Since the quaternion exponential function agrees with the real and complex exponential function of real and complex arguments, it follows that the quaternion hyperbolic functions also agree with their usual counterparts for real and complex input. This allows us to discuss some important hyperbolic identities and the existence of infinitely many zeros of the quaternion sine and cosine hyperbolic functions, and to solve equations involving hyperbolic functions. A remarkable result of the theory exhibits the deep connection between the hyperbolic and trigonometric functions discussed in the previous chapter. We hope that material presented in this part will make this beautiful topic accessible to the reader.

Keywords: Trigonometric Function; Cosine Function; Hyperbolic Function; Previous Chapter; Complex Exponential Function (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-0348-0622-0_7

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