Matrix-valued little q-Jacobi polynomials

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2×2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and their relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on a matrix-valued q-difference operator, which is a q-analogue of Tirao’s matrix-valued hypergeometric differential operator.Netherlands Organisation for Scientific ResearchBelgian Interuniversity Attraction Pole DygestMinisterio de Economía y CompetitividadJunta de Andalucí