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Abstract. Bounds are proved for the Stieltjes polynomial E n+1 , and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. 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 PnE n+1 in the uniform and weighted L p norms. The corresponding Lebesgue constants are of optimal order.

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