Ratio and Plancherel-Rotach asymptotics for Meixner-Sobolev orthogonal polynomials

We study the analytic properties of the monic Meixner-Sobolev polynomials {Q(n)} orthogonal with respect to the inner product involving differences [GRAPHICS] where lambda greater than or equal to 0, Delta is the forward difference operator (Delta f(x) = f(x + 1) - f(x)) and (gamma)(n) denotes the Pochhammer symbol. Relative asymptotics for Meixner-Sobolev polynomials with respect to Meixner polynomials is obtained. This relative asymptotics is also given for the scaled polynomials. Moreover, a zero distribution for the scaled Meixner-Sobolev polynomials and Plancherel-Rotach asymptotics for {Q(n)} are deduced. (C) 2000 Elsevier Science B.V. All rights reserved.