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Inverse Hyperbolic and Trigonometric Functions

In: Real Quaternionic Calculus Handbook

Author

Listed:
  • 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)

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.

Suggested Citation

  • João Pedro Morais & Svetlin Georgiev & Wolfgang Sprößig, 2014. "Inverse Hyperbolic and Trigonometric Functions," Springer Books, in: Real Quaternionic Calculus Handbook, edition 127, chapter 8, pages 125-132, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0622-0_8
    DOI: 10.1007/978-3-0348-0622-0_8
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