Hypermonogenic Functions of Two Vector Variables

摘要

In this paper we introduce the modified Dirac operators and , where is differentiable function, and is the Clifford algebra generated by the basis vectors of . We look for solutions of the system , where the first and third variables are invariant under rotations. These functions are called -hypermonogenic functions. We discuss about axially symmetric functions with respect to the symmetric group . Some examples of axially symmetric -hypermonogenic functions generated by homogeneous functions and hypergeometric functions are presented.