A Problem in Potential Theory and Zero Asymptotics of Krawtchouk Polynomials

Abstract

In this paper we investigate the asymptotics of the zeros of normalized Krawtchouk polynomials kn(Nx, p, N) when the ratio of the parameters n/N→α as n, N→∞. For this purpose we consider in detail a particular constrained energy problem on the interval [0, 1] in the presence of an external field. We find the support and the density of the constrained extremal measure for all possible values of the parameter α. © 2000 Academic Press.