Contracted Zero Distributions of Extremal Polynomials Associated with Slowly Decaying Weights

We consider the asymptotic zero behavior of polynomials that are extremal with respect to slowly decaying weights on [0, ∈fty) , such as the log-normal weight exp(-γ ² log  ² x) . The zeros are contracted by taking the appropriate d _n th roots with d _n →∈fty . The limiting distribution of the contracted zeros is described in terms of the solution of an extremal problem in logarithmic potential theory with a circular symmetric external field. November 23, 1998. Date revised: February 8, 1999. Date accepted: March 2, 1999.