Monogenic Polynomials of Four Variables with Binomial Expansion

  • Carla Cruz
  • M. Irene Falcão
  • Helmuth R. Malonek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8579)


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.


monogenic polynomials Appell sequences pseudo-complex powers 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Carla Cruz
    • 1
  • M. Irene Falcão
    • 2
  • Helmuth R. Malonek
    • 1
    • 3
  1. 1.Centro de Investigação e Desenvolvimento em Matemática e AplicaçõesUniversidade de AveiroPortugal
  2. 2.Departamento de Matemática e Aplicações and Centro de MatemáticaUniversidade do MinhoPortugal
  3. 3.Departamento de MatemáticaUniversidade de AveiroPortugal

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