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

Abstract

In this paper, we present the algebraic properties of dual quaternions and define a slice regularity of a dual quaternionic function. Since the product of dual quaternions is non-commutative, slice regularity is derived in two ways. Thereafter, we propose the Cauchy-Riemann equations and a power series corresponding to dual quaternions.

Keywords

• dual number
• quaternion
• cauchy-riemann equation
• slice regular function
• clifford analysis