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Remarks on the generation of monogenic functions
Cruz, J. F.; Falcão, M. I.; Malonek, H. R.In this paper we consider three different methods for generating monogenic functions. The first one is related to Fueter's well known approach to the generation of monogenic quaternion-valued functions by means of holomorphic functions, the second one is based on the solution of hypercomplex differential equations and fnally the third one is a direct series approach, based on the use of special homogeneous poly...
3D-mappings and their approximations by series of powers of a small parameter
Cruz, J. F.; Falcão, M. I.; Malonek, H. R.Conformal mappings in the plane are closely linked with holomorphic functions and their property of complex differentiability. In contrast to the planar case, in higher dimensions the set of conformal mappings consists only of M¨obius transformations which are not monogenic and therefore also not hypercomplex differentiable. But due to the equivalence between being hypercomplex differentiable and being monogeni...
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