In this talk we introduce a class of orthogonal polynomials with N-periodically modulated Jacobi parameters. The class is sufficiently large to contain many classical polynomials such as Hermite, Meixner—Pollaczek, Laguerre. We implement a program in which we study convergence of generalized Tur\'an determinants, approximation of the density of the orthogonality measure, uniform asymptotic behavior of orthogonal polynomials as well as Christoffel--Darboux kernels. We also study the asymptotic distribution of zeros. The talk is based on joint works with Grzegorz Świderski (Polish Academy of Sciences & University of Wroclaw).
