HYPERHOLOMORPHIC FUNCTIONS WITH VALUES IN A MODIFIED FORM OF QUATERNIONS

摘要

We give the definition of hyperholomorphic pseudo-complex functions, i.e., functions with values in a special form of quaternions, and propose the necessary variables, functions, and Dirac operators to describe the Cauchy integral theorem and the generalized Cauchy-Riemman system. We investigate the properties and corollaries corresponding to the Cauchy integral theorem for the pseudo-complex number system discussed in this paper.