On generalized stieltjes polynomials and Lagrange interpolation

We prove, for the ultraspherical weight function w(lambda)(x) = (1-x(2))(lambda-1/2), new inequalities for generalized Stieltjes polynomials, and apply them to obtain convergence results, in the uniform and weighted L(p) norms, for the Lag-range interpolation process based on the zeros of generalized Stieltjes polynomials and the extended Lagrange interpolation process using the zeros of ultraspherical polynomials and Stieltjes polynomials. In particular, we show that the extended interpolation process has Lebesgue constants of optimal order (O(log n) for 0 less than or equal to lambda less than or equal to 1/2, while for 1/2 < lambda less than or equal to 1, they are of order O(n(2 lambda-1)).