Approximation properties of polynomials ln,n(x), orthogonal on any sets

Let Ω={x0,x1,…,xj,…} - discrete system of points such that 0=x0 0 on arbitrary grids consisting of an infinite many points on the semi-axis [0,+∞) are investigated. Namely an asymptotic formula is proved in which asymptotic behavior of these polynomials as n tends to infinity together with N is closely related to asymptotic behavior of the orthonormal Laguerre polynomials L^αn(x).