Three-term recurrence relations for systems of Clifford algebra-valued orthogonal polynomials

摘要

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.