Inverse Hyperbolic and Trigonometric 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 8 in Real Quaternionic Calculus Handbook, 2014, pp 125-132 from Springer

Abstract: Abstract The main focus of this chapter is to study the inverses of the quaternion trigonometric and hyperbolic functions, and their properties. Since the quaternion trigonometric and hyperbolic functions are defined in terms of the quaternion exponential function e p , it can be shown that their inverses are necessarily multi-valued and can be computed via the quaternion natural logarithm function ln(p). The s facts we shall see here attest the great interest of these functions in mathematics. Proofs of the most known facts are ommited.

Keywords: Cosine Function; Hyperbolic Function; Tangent Function; Inverse Tangent; Real Quaternion (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-0348-0622-0_8

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