Modified (0,2)-interpolation ion the roots of Jacobi polynomials.: II (convergence)

In [4] A. M. Chak, A. Sharma and J. Szabados characterized the Jacobi matrices P(alpha, beta), (alpha,beta > -1) for which the (0, 2)-interpolation problem is regular. It follows from their result, that if n is odd and alpha = beta, or if alpha,beta are both odd integers and n > 1+ (alpha +beta)/2, then the (0, 2)-interpolation problem is not regular. Recently, the author proved that for alpha,beta both odd integers, the (0, 2)-interpolation problem augmented with boundary (Hermite-type) conditions at the endpoints of the interval [-1, 1] is regular. In this paper the convergence of this modified (0, 2)-interpolation procedure is studied, if the inner nodal points are the roots of the ultraspherical polynomials with odd integer parameter.