Let N be a natural number greater than 1. We select N uniformly distributed points t_k = 2πk/N (0 < k < N − 1) on [0,2\pi]. Denote by L_ n,N (f) = L _n,N (f,x)1 < n < ⌊N/2⌋ the trigonometric polynomial of order n possessing the least quadratic deviation from f with respect to the system tk{k=0}^{N-1}. In other words, the greatest lower bound of the sums on the set of trigonometric polynomials Tn of order n is attained by L_n,N (f). In the present article the problem of function approximation by the polynomials L_n,N (f,x) is considered.
