Generalized-Analytical Functions of Poly-Number Variable

Abstract

We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in theoretical physical constructions. As an example we consider in detail the associative-commutative hypercomplex numbers $H_4$ and an interesting class of corresponding functions.

16 pages, no figures