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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.14 no.2 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000200004 

CUBO A Mathematical Journal Vol.14, No 02, (61-80). June 2012

Texto completo disponíble en formato PDF

Bicomplex Numbers and their Elementary Functions

 

M.E. LUNA-ELIZARRARÁS*, M. SHAPIRO*, D.C. STRUPPA1**, A. VAJIAC**

*Departamento de Matemáticas, E.S.F.M del I.P.N., Mexico.

**Schmid College of Science and Technology, Chapman University, Orange California, 1 email: struppa@chapman.edu


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.

Keywords and Phrases: Bicomplex numbers, Elementary functions


RESUMEN

En este artículo introducimos el algebra de números bicomplejos como una generalizacion del campo de números complejos. Describimos como definir funciones elementales en tales algebras (polinomios y funciones exponenciales y trigonometricas) así como sus funciones inversas (raíces, logaritmos, funciones trigonométricas inversas). Nuestro objetivo es mostrar que una teoría de funciones sobre numeros bicomplejos es, en cierto sentido, una mejor generalización de la teoría de funciones holomorfas de una variable compleja, que la teorúía de funciones holomorfas en dos variables complejas.

2010 AMS Mathematics Subject Classification: 30G35


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Received: May 2011. Revised: October 2011.