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Published in:
2013 | OriginalPaper | Chapter
A Note on Totally Regular Variables and Appell Sequences in Hypercomplex Function Theory
Authors : Carla Cruz, M. Irene Falcão, Helmuth R. Malonek
Published in: Computational Science and Its Applications – ICCSA 2013
Publisher: Springer Berlin Heidelberg
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The aim of our contribution is to call attention to the relationship between totally regular variables, introduced by R. Delanghe in 1970, and Appell sequences with respect to the hypercomplex derivative. Under some natural normalization condition the set of all paravector valued totally regular variables defined in the three dimensional Euclidean space will be completely characterized. Together with their integer powers they constitute automatically Appell sequences, since they are isomorphic to the complex variables.