On the Limit Distributions of the Zeros of Jonquière Polynomials and Generalized Classical Orthogonal Polynomials Original Research Article

Jonquière polynomials Jk are defined by the rational function ∑∞0nkzn = Jk(z)/(1 − z)k+1, k ∈ N0. For a general class of polynomials including Jk, 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(αn, βn)n, L(αn)n, and H(αn)n with degree dependent parameters αn, βn by using a continued fraction technique. In this paper these limit distributions are derived via a differential equation approach.