On Lagrange interpolation with equally spaced nodes

A well-known result due to S.N. Bernstein is that the sequence of Lagrange interpolation polynomials for \x\ at equally spaced nodes in [-1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for \x\(3) at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.