, Volume 7, Issue 5, pp 1675-1711

Complex Laplacian and Derivatives of Bicomplex Functions

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Abstract

In this paper we study in detail the theory of bicomplex holomorphy, in the context of the several ways in which bicomplex numbers can be considered. In particular we will show how the notions of bicomplex derivability and bicomplex holomorphy can be interpreted in these different ways, and the consequences that can be derived.

Communicated by Daniel Aron Alpay.
M. E. Luna-Elizarrarás and M. Shapiro have been partially supported by CONACYT projects as well by Instituto Politécnico Nacional in the framework of COFAA and SIP programs. All the four authors are grateful to Chapman University for the support offered in preparing the final stages of this article.