Stieltjes polynomials and Lagrange interpolation

Bounds are proved for the Stieltjes polynomial E(n+2), and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials P-n. This sharpens a known interlacing result of Szego. As a byproduct, bounds are obtained for the Geronimus polynomials G(n). Applying these results; convergence theorems are proved for the Lagrange interpolation process with respect to the zeros of E(n+1), and for the extended Lagrange interpolation process with respect to the zeros of P(n)E(n+1) in the uniform and weighted L(P) norms. The corresponding Lebesgue constants are of optimal order.