A New Theory of Regular Functions of a Quaternionic Variable
In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.
Gentili, G., & Struppa, D.C. (2007, December). A New Theory of Regular Functions of a Quaternionic Variable. Advances in Mathematics, 216(1), 279–301. doi: 10.1016/j.aim.2007.05.010