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Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials

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Abstract

Recently, systems of Clifford algebra-valued orthogonal polynomials have been studied from different points of view. We prove in this paper that for their building blocks there exist some three-term recurrence relations, similar to that for orthogonal polynomials of one real variable. As a surprising byproduct of own interest we found out that the whole construction process of Clifford algebra-valued orthogonal polynomials via Gelfand–Tsetlin basis or otherwise relies only on one and the same basic Appell sequence of polynomials.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    I. Cação & H. R. Malonek

  2. Department of Mathematics and Applications, Centre of Mathematics, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    M. I. Falcão

Authors
  1. I. Cação
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  2. M. I. Falcão
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  3. H. R. Malonek
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Correspondence to H. R. Malonek.

Additional information

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

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Cação, I., Falcão, M.I. & Malonek, H.R. Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials. Adv. Appl. Clifford Algebras 27, 71–85 (2017). https://doi.org/10.1007/s00006-015-0596-z

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  • DOI: https://doi.org/10.1007/s00006-015-0596-z

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