On the φ-Hyperderivative of the ψ-Cauchy-Type Integral in Clifford Analysis

The aim of this paper is to introduce, in the framework of Clifford analysis, the notions of phi-hyperdifferentiability and phi-hyperderivability for psi-hyperholomorphic functions where (phi, psi) are two arbitrary orthogonal bases (called structural sets) of a Euclidean space. In this study we will also show how to exchange the integral sign and the phi-hyperderivative of the psi-Cliffordian Cauchy-type integral. Thereby, we generalize, in a natural way, the corresponding quaternionic antecedent as well as the standard Clifford predecessor.