Bicomplex Numbers and their Elementary Functions
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M. E. Luna
struppa@chapman.edu
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M. Shapiro
struppa@chapman.edu
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D. C. Struppa
struppa@chapman.edu
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A. Vajiac
struppa@chapman.edu
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DOI:
https://doi.org/10.4067/S0719-06462012000200004Abstract
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.
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Published
2012-06-01
How to Cite
[1]
M. E. Luna, M. Shapiro, D. C. Struppa, and A. Vajiac, “Bicomplex Numbers and their Elementary Functions”, CUBO, vol. 14, no. 2, pp. 61–80, Jun. 2012.
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