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Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 71–85 | Cite as

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

Article

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.

Mathematics Subject Classification

Primary 30G35 Secondary 32A05 

Keywords

Clifford analysis Generalized Appell polynomials Recurrence relations 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

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

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