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Cubo (Temuco)

On-line version ISSN 0719-0646

Abstract

LUNA-ELIZARRARAS, M.E; SHAPIRO, M; STRUPPA, D.C  and  VAJIAC, A. Bicomplex Numbers and their Elementary Functions. Cubo [online]. 2012, vol.14, n.2, pp. 61-80. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462012000200004.

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.

Keywords : Bicomplex numbers; Elementary functions.

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