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Title: On paravector valued homogeneous monogenic polynomials with binomial expansion
Author: Malonek, Helmuth Robert
Falcão, Maria Irene
Keywords: Clifford analysis
Generalized Appell polynomial
Issue Date: Sep-2012
Publisher: SP Birkhäuser Verlag Basel
Abstract: The aim of this note is to study a set of paravector valued homogeneous monogenic polynomials that can be used for a construction of sequences of generalized Appell polynomials in the context of Clifford analysis. Therefore, we admit a general form of the vector part of the first degree polynomial in the Appell sequence. This approach is different from the one presented in recent papers on this subject. We show that in the case of paravector valued polynomials of three real variables, there exist essentially two different types of such polynomials together with two other trivial types of polynomials. The proof indicates a way of obtaining analogous results in the case of polynomials of more than three variables.
Peer review: yes
DOI: 10.1007/s00006-012-0361-5
ISSN: 0188-7009
Appears in Collections:CIDMA - Artigos

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