Regularity for quaternion functions of several complex variables (Q1097371)

The authors first give some relations between right- and left-regular functions \((fD=0\) resp. \(Df=0)\) as well as real harmonic functions of a quaternion variable \[ z=x_ 1i+x_ 2j+x_ 3k+x_ 4 \] using \[ D=\frac{\partial}{\partial x_ 1}i+\frac{\partial}{\partial x_ 2}j+\frac{\partial}{\partial x_ 3}k+\frac{\partial \quad}{\partial x_ 4}. \] These results seem to be scattered in the litterature. An example of an exponential function is given, here one should refer to a paper by \textit{F. Sommen} [Appl. Anal. 12, 13-36 (1981; Zbl 0454.30039)].