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Monogenic Polynomials of Four Variables with Binomial Expansion

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Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8579))

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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.

This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, the Research Centre of Mathematics of the University of Minho and the Portuguese Foundation for Science and Technology (“FCT - Fundação para a Ciência e a Tecnologia”), within projects PEst-OE/MAT/UI4106/2014 and PEstOE/MAT/UI0013/2014.

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Author information

Authors and Affiliations

  1. Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Universidade de Aveiro, Portugal

    Carla Cruz & Helmuth R. Malonek

  2. Departamento de Matemática e Aplicações and Centro de Matemática, Universidade do Minho, Portugal

    M. Irene Falcão

  3. Departamento de Matemática, Universidade de Aveiro, Portugal

    Helmuth R. Malonek

Authors
  1. Carla Cruz
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  2. M. Irene Falcão
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  3. Helmuth R. Malonek
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Editor information

Editors and Affiliations

  1. School of Engineering, University of Basilicata, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Computer and Information Sciences, Covenant University, Ota, Nigeria

    Sanjay Misra

  3. Department of Production and Systems, University of Minho, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha

  4. DICAR, Polytecnico di Bari, 70125, Bari, Italy

    Carmelo Torre

  5. University of Minho, Braga, Portugal

    Jorge Gustavo Rocha  & Maria Irene Falcão  & 

  6. Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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Cruz, C., Falcão, M.I., Malonek, H.R. (2014). Monogenic Polynomials of Four Variables with Binomial Expansion. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8579. Springer, Cham. https://doi.org/10.1007/978-3-319-09144-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-09144-0_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09143-3

  • Online ISBN: 978-3-319-09144-0

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