New Characterizations of Discrete Classical Orthogonal Polynomials Original Research Article

We prove that if both {Pn(x)}∞n=0and {∇r Pn(x)}∞n=rare orthogonal polynomials for any fixed integer r⩾1, then {Pn(x)}∞n=0must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahnʹs theorem stating that if both {Pn(x)}∞n=0and {(d/dx)r Pn(x)}∞n=rare orthogonal polynomials, then {Pn(x)}∞n=0are classical orthogonal polynomials. We also obtain several other characterizations of discrete classical orthogonal polynomials.