Abstract
The corresponding Cauchy-Riemann system for dual quaternion-valued functions
Highlights
A dual quaternion can be represented in the form p + εq, where p and q are ordinary quaternions and ε is the so-called dual unit, an element that commutes with every element of the algebra and is such that ε2 = 0
The set of dual quaternions is the following Clifford algebra: Dq := {Z = p1 + εp2 | p1, p2 ∈ H}, where H is the set of quaternions which are combined by the basis elements 1, i, j, k
We give a norm for a quaternion as follows: |p|2 := pp∗ = z1z1 + z2z2 and the inverse of p as follows: p−1 = p∗ |p|2 (p = 0)
Summary
The set of dual quaternions is the following Clifford algebra: Dq := {Z = p1 + εp2 | p1, p2 ∈ H}, where H is the set of quaternions which are combined by the basis elements 1, i, j, k. Kim et al [10] obtained a corresponding inverse of functions and their properties and a regularity of functions on the form of multidual complex variables in Clifford analysis. The paper represents a corresponding Cauchy theorem of dual quaternion-valued functions by using a dual Cauchy – Riemann system in dual quaternions.
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