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)=zn+⋯ be the monic nth-degree polynomial satisfying the planar orthogonality condition ∫DPn(z)zm¯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 norm ∫D|Pn|2dxdy.
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