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Advances in Applied Clifford Algebras

, Volume 22, Issue 3, pp 789–801 | Cite as

On Paravector Valued Homogeneous Monogenic Polynomials with Binomial Expansion

  • H. R. Malonek
  • M. I. FalcãoEmail author
Article

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.

Mathematics Subject Classification (2010)

Primary 30G35 Secondary 32A05 

Keywords

Clifford analysis generalized Appell polynomial 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal
  3. 3.Department of Mathematics and ApplicationsUniversity of MinhoBragaPortugal

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