In this article asymptotic properties of the Chebyshev polynomials Tn(x,N) (0 ≤ n ≤ N − 1) orthogonal on an uniform net ΩN = {0,1,...,N − 1} with the constant weight µ(x) = 2 N (discrete analog of the Legendre polynomials) by n = O(N 1 2 ), N → ∞ were researched. The asymptotic formula that is relating polynomials Tn(x,N) with Legendre polynomials Pn(t) for x = N 2 (1 + t) − 1 2 was determined.
