On Connection Coefficients of d-Orthogonal Polynomials in Terms of Orthogonal Polynomials and the Canonical Basis

In this work, we address the problem of expressing sequences of d d -orthogonal polynomials in terms of either orthogonal polynomials or the canonical basis. We derive a general recurrence relation that enables the symbolic recursive computation of these coefficients. Several results are established to investigate the impact of the Appell character, as well as the symmetry and d d -symmetry of the polynomial sequences, on these coefficients. Additionally, we deduce some results concerning the zeros of d d -orthogonal polynomials.