A survey on the (hyper-) derivatives in complex, quaternionic and Clifford analysis (Q653922)

In this survey article, a hyperderivative of quaternion or Clifford algebra valued functions, generalizing holomorphic functions, is studied. A hyperderivative is based on the quaternion case of \textit{A. Sudbery} [Math. Proc. Camb. Philos. Soc. 85, 199--225 (1979; Zbl 0399.30038)]. In Clifford algebras, the hyper-complex derivative for monogenic functions is defined by \textit{K. Gürlebeck} and \textit{H. Malonek} in [Complex Variables, Theory Appl. 39, No. 3, 199--228 (1999; Zbl 1019.30047)]. The goal of the paper is to explain that the hyperderivative is the direct generalization of the complex derivative of the holomorphic function in the complex plane.