Hyperholomorphic functions with values in a modified form of quaternions

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.