Asymptotic properties of polynomials pˆn(t), orthogonal with weight ∆tj on any finite set of N points from segment [−1, 1] 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 Lasiandra polynomials. Furthermore are investigated the approximating properties of the sums by Fourier on these polynomials..
