On the Sharpness of Theorems Concerning Zero-Free Regions for Certain Sequences of Polynomials,

摘要

In this paper, the authors establish the sharpness of a theorem concerning zero-free parabolic regions for certain sequences of polynomials satisfying a three-term recurrence relation. Similarly, the authors establish the sharpness of a zero-free sectorial region for certain sequences of Pade approximants to (e sup z).