A Polar Representation of a Regularity of a Dual Quaternionic Function in Clifford Analysis

Abstract

Abstract. The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.

Application of slice regularity to functions of a dual-quaternionic variable

“…J.E. Kim et al [7,8] investigated the extended the regularity of dual quaternionic functions and represented dual quaternionic functions by using various forms such as their polar form in Clifford analysis. This study shows that the generalized Cullen definition can be applied to the set of dual quaternions and that theories of slice regular functions can be applied to dual quaternions.…”