A structure relation for some specific orthogonal polynomials

Abstract

By characterizing all orthogonal polynomials sequences (Pn) n≥0 for whichwhere I is the identity operator, x defines a q-quadratic lattice, △f (s) = f (s + 1) − f (s), and (an) n≥0 , (bn) n≥0 and (cn) n≥0 are sequences of complex numbers, we derive some new structure relations for some specific families of orthogonal polynomials.