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 {Pn, Qn}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.