Advances in Applied Clifford Algebras

, Volume 24, Issue 4, pp 981–994 | Cite as

A Matrix Recurrence for Systems of Clifford Algebra-Valued Orthogonal Polynomials

  • I. Cação
  • M. I. Falcão
  • H. R. MalonekEmail author


Recently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of Hypercomplex Function Theory (Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory, 12 (2012), no. 2, 371-391). This paper deals with an extension of that approach to a recurrence relation for the construction of a complete system of orthogonal Clifford-algebra valued polynomials of arbitrary degree. At the same time the matrix approach sheds new light on results about systems of Clifford algebra-valued orthogonal polynomials obtained by Gürlebeck, Bock, Lávička, Delanghe et al. during the last five years. In fact, it allows to prove directly some intrinsic properties of the building blocks essential in the construction process, but not studied so far.


Clifford Analysis generalized Appell polynomials recurrence relations 


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© Springer Basel 2014

Authors and Affiliations

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

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