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Generalized Derivative and Primitive of Cliffordian Bases of Polynomials Constructed Through Appell Monomials

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Abstract

In the present paper the authors treat two different problems. They start by answering the question posed in [5] concerning the structure of derivative bases, then investigate the convergence properties (the effectiveness) of the generalized derivative and primitive of a given base of polynomials with values in a Clifford algebra. Finally, they study the mode of increase of such derivatives and primitive bases.

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Authors and Affiliations

  1. Department of Mathematics, King Khalid University, Abha, Saudi Arabia

    Mohra Zayed

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    Mahmoud Abul-Ez

  3. Institute of Applied Analysis, Freiberg University of Mining and Technology, 09596, Freiberg, Germany

    João Pedro Morais

Authors
  1. Mohra Zayed
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  2. Mahmoud Abul-Ez
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  3. João Pedro Morais
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Corresponding author

Correspondence to Mohra Zayed.

Additional information

The third author’s research is supported by Foundation for Science and Technology (FCT) via the post-doctoral grant SFRH/BPD/66342/2009.

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Zayed, M., Abul-Ez, M. & Morais, J.P. Generalized Derivative and Primitive of Cliffordian Bases of Polynomials Constructed Through Appell Monomials. Comput. Methods Funct. Theory 12, 501–515 (2012). https://doi.org/10.1007/BF03321840

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