Bicomplex Numbers and Their Elementary Functions

Authors

M. E. Luna-Elizarrarás, E.S.F.M
M. Shapiro, E.S.F.M
Daniele C. Struppa, Chapman UniversityFollow
Adrian Vajiac, Chapman UniversityFollow

Document Type

Article

Publication Date

2012

Abstract

In this paper we introduce the algebra of bicomplex numbers as a generalization of the field of complex numbers. We describe how to define elementary functions in such an algebra (polynomials, exponential functions, and trigonometric functions) as well as their inverse functions (roots, logarithms, inverse trigonometric functions). Our goal is to show that a function theory on bicomplex numbers is, in some sense, a better generalization of the theory of holomorphic functions of one variable, than the classical theory of holomorphic functions in two complex variables.

Comments

This article was originally published in CUBO, volume 14, issue 2, in 2012. DOI: 10.4067/S0719-06462012000200004

Recommended Citation

Luna-Elizarraras, M.E, Shapiro, M., Struppa, D.C., & Vajiac, A. (2012). Bicomplex Numbers and their Elementary Functions. CUBO, 14(2), 61-80. doi: 10.4067/S0719-06462012000200004

Peer Reviewed

1

Copyright

Cubo