A Structure Relation for Some Orthogonal Polynomials

We describe all orthogonal polynomial sequences (P-n) n >= 0 for which (ax vertical bar b)(Delta vertical bar 2I)P-n(x(s - 1/2)) = (a(n)x vertical bar b(n))Pn(x) + c(n)P(n-1)(x), where I is the identity operator, x defines a q-quadratic lattice, Delta f(s) = f(s+ 1) - f(s), and (a(n))(n >= 0), (b(n))(n >= 0) and (c(n))(n >= 0) are sequences of complex numbers. We also derive new structure relations for some families of orthogonal polynomials.