Asymptotics of Polynomials Orthogonal on a Cross with a Jacobi-type Weight

Abstract

We investigate asymptotic behavior of polynomials $Q_n(z)$ satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)\dd s =0, \quad k\in\{0,\ldots,n-1\}, $$ where $ Δ:= [-a,a]\cup [-\ic b,\ic b] $, $a,b>0$, and $\rho (s)$ is a Jacobi-type weight.