Asymptotic normality of the coefficients of polynomials associated with the Gegenbauer ones

摘要

A suitable transformation on the classical Gegenbauer orthogonal polynomials leads to polynomials with nonnegative coefficients. Asymptotic normality of those coefficients is established and rate of convergence and asymptotic formulas are provided. As examples the number of matching sets of paths and polygons, respectively, are approximated.