Influence of the choice of Lagrange interpolation nodes on the exact and approximate values of the Lebesgue constants

The behavior of the Lebesgue constants corresponding to two classical Lagrange interpolation polynomials is studied in dependence on the number of interpolation nodes uniformly distributed on the period divided into three classes. We obtain new exact and approximate formulas for the constants corresponding to each of these classes: the errors are estimated uniformly in the degree of a polynomial. Two standing problems are solved in interpolation theory that are connected with asymptotic equalities for Lebesgue constants.