Bicomplex Numbers and their Elementary Functions

By M. E. Luna-Elizarrar'as, M. Shapiro, Daniele C. Struppa, A. Vajiac. 2012

134 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3a854eaeb5e131d711326320e80c4143ea36beb6

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Bicomplex holomorphic functional calculus (2014, background): “In this section we summarize the main properties of bicomplex numbers and of holomorphic functions of bicomplex numbers, and we refer the reader to [5], [10], [11], [12], [13], [14] for further details.”
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis (2013, background): “those functions on the ring BC of bicomplex numbers, whose properties suggest a notion of bicomplex holomorphy. Rather than giving an exhaustive list of references, we refer the reader to the article [35] and to the forthcoming monograph [37]. As demonstrated in these references (as well as in the m”