TY: JOUR T1 - The Static Maxwell System in Three Dimensional Axially Symmetric Inhomogeneous Media and Axially Symmetric Generalization of the Cauchy?Riemann System A1 - Bryukhov, Dmitry A1 - Kähler, Uwe N2 - In this paper we discuss different generalizations of the Cauchy?Riemann system and their connection with the static Maxwell system. In particular, this allows us to present relations between slice-monogenic functions and hypermonogenic functions, as well as to provide a physical interpretation of slice-monogenic functions. Furthermore, we present an explicit and complete set of basic solutions of a new class of axial-hypermonogenic functions in R^3. In the end we determine the symmetry operators for the class of axial-hypermonogenic functions. UR - https://ria.ua.pt/handle/10773/18247 Y1 - 2017 PB - Birkhaeuser