On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

摘要

We study the asymptotic zero distribution of Laguerre L_n~((α_n)) and generalized Bessel B_n~((α_n)) polynomials with the parameter α_n varying in such a way that the limit of α_n exists. Our approach is based on a non-hermitian orthogonality satisfied by these sequences of polynomials. In the cases that remain open we formulate the corresponding conjectures.