Polar Coordinate Expression of Hyperholomorphic Functions on Split Quaternions in Clifford Analysis

Abstract

This paper defines a hyperholomorphic function and a split harmonic function with values in split quaternions, expresses polar coordinate forms for split quaternions, and obtains some split Cauchy–Riemann systems that are equivalent. The paper provides split hyperholomorphic mappings on \({\Omega\subset \mathbb{C}^2}\) and researches the properties of split hyperholomorphic mappings.