Dual quaternion functions and its applications (Q1790015)

Summary: A dual quaternion is associated with two quaternions that have basis elements \(e_0\), \(e_1\), \(e_2\), \(e_3\), and \(\varepsilon\). Dual numbers are often written in the form \(z=\zeta+\varepsilon\zeta^\ast\), where \(\varepsilon\) is the dual identity and has the properties \(\varepsilon^2=0\) \((\varepsilon\neq0)\). We research the properties of some regular functions with values in dual quaternion and give applications of the extension problem for dual quaternion functions.