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Hyperbolic 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

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.

Suggested Citation

  • João Pedro Morais & Svetlin Georgiev & Wolfgang Sprößig, 2014. "Hyperbolic Functions," Springer Books, in: Real Quaternionic Calculus Handbook, edition 127, chapter 7, pages 117-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0622-0_7
    DOI: 10.1007/978-3-0348-0622-0_7
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