Representation of some classes of quaternionic hyperholomorphic functions

Abstract

In the algebra of complex quaternions H(C) we consider the left- and right-ψ-hyperholomorphic functions, and left-Λ — ψ-hyperholomorphic functions. We justify the transition in left- and right-ψ-hyperholomorphic functions to a simpler basis i.e., to the Cartan basis. Using Cartan's basis we find the solution of Cauchy-Fueter equation. By the same method we find representations of left- and right-ψ-hyperholomorphic functions, and representation of left-Λ — ψ-hyperholomorphic functions.