About asymptotic polynomials, orthogonal on any grids

Asymptotic properties of polynomials orthogonal $l_n(x),$ with weight $e^{-x_j}\Delta t_j$ on any infinite set points from semi-axis $[0,\infty)$ are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as $n$ tends to infinity together with $N$ is closely related to asymptotic behaviour of the polynomials by Lagerra.