Matrix-Valued Little q-Jacobi Polynomials

TL;DR

This paper introduces matrix-valued little q-Jacobi polynomials, providing explicit formulas and relations to hypergeometric series, expanding the theory of orthogonal polynomials into matrix-valued q-analogues.

Contribution

It develops the first comprehensive study of matrix-valued little q-Jacobi polynomials, including explicit formulas and their connection to matrix-valued q-hypergeometric series.

Findings

Explicit orthogonality relations derived

Rodrigues formula established

Three-term recurrence relation identified

Abstract

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2x2-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.