Abstract:Let D be a domain obtained by removing, out of the unit disk {z : |z| < 1}, finitely many mutually disjoint closed disks, and for each integer n ≥ 0, let Pn(z) = z n + · · · be the monic nth-degree polynomial satisfying the planar orthogonality condition´D Pn(z)z m dxdy = 0, 0 ≤ m < n. Under a certain assumption on the domain D, we establish asymptotic expansions and formulae that describe the behavior of Pn(z) as n → ∞ at every point z of the complex plane. We also give an asymptotic expansion for the squared… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.