ON THE LIMIT DISTRIBUTIONS OF THE ZEROS OF JONQUIERE POLYNOMIALS AND GENERALIZED CLASSICAL ORTHOGONAL POLYNOMIALS

Jonquiere polynomials J(k) are defined by the rational function Sigma(0)(infinity) n(k)z(n) = J(k)(z)/(1 - z)(k+1), k is an element of N-0. For a general class of polynomials including J(k), the limit distribution of its zeros is computed. Recently Dette and Studden have found the asymptotic zero distributions for Jacobi, Laguerre, and Hermite polynomials p(n)((alpha n,beta n)), L(n)((alpha n)), and H-n((alpha n)) with degree dependent parameters alpha(n), beta(n) by using a continued fraction technique. In this paper these limit distributions are derived via a differential equation approach. (C) 1995 Academic Press, Inc.