Matrix-valued little q-Jacobi polynomials

• Published in: Journal of approximation theory Vol. 193; pp. 164 - 183
• Main Authors: Aldenhoven, Noud, Koelink, Erik, de los Ríos, Ana M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2015
• Subjects: Little [formula omitted]-Jacobi polynomials; Matrix-valued [formula omitted]-difference operators; Matrix-valued orthogonal polynomials; Little q-Jacobi polynomials; Matrix-valued q-difference operators; Matrix-valued orthogonal polynomials
• ISSN: 0021-9045; 1096-0430
• DOI: 10.1016/j.jat.2014.10.007

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.