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Title: Monogenic polynomials of four variables with binomial expansion
Author: Cruz, Carla
Falcão, Maria Irene
Malonek, Helmuth Robert
Keywords: Monogenic polynomials
Appell sequences
Pseudo-complex powers
Issue Date: 2014
Publisher: Springer International Publishing
Abstract: In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.
Peer review: yes
DOI: 10.1007/978-3-319-09144-0_15
ISBN: 978-3-319-09143-3
ISSN: 0302-9743
Appears in Collections:CIDMA - Comunicações

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