Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice x(s) = q2s

AbstractWe give explicitly recurrence relations satisfied by the connection coefficients between two families of the classical orthogonal polynomials of a discrete variable on a non-uniform lattice x(s) = q2s (i.e., the q-analogues of Charlier, Meixner, Krawtchouk and Hahn polynomials), in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ρ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by these polynomials