An asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle

摘要

We consider the system of biorthogonal polynomials {P-n, Q(n)}(n) >= 0 with respect to a complex valued measure supported on the unit circle and give a uniform compound asymptotic expansion formula consisting of the sum of two inverse factorial series, giving the explicit expression of the terms and including error bounds. As a consequence we prove that the set of accumulation points of the zeros these polynomials is included in the unit circle. Some numerical experiments are included. (C) 2017 Elsevier Inc. All rights reserved.