Comparative asymptotics for discrete semiclassical orthogonal polynomials

We study the ratio P-n(x;z)/phi(n)(x) asymptotically as n -> infinity, where the polynomials P-n(x; z) are orthogonal with respect to a discrete linear functional and phi(n)(x) denote the falling factorial polynomials. We give recurrences that allow the computation of high order asymptotic expansions of P-n(x; z) and give examples for most discrete semiclassical polynomials of class s <=( )2. We show several plots illustrating the accuracy of our results.