Abstract
We investigate in this paper the geometric convergence of the Lagrange and Hermite interpolation processes and the Gauss-Jacobi quadrature formula of an entire function and its higher derivatives when the nodes of interpolation are taken to be the zeros of the orthogonal polynomials associated with the very smooth Freud weight w α(x) = exp(−2¦x¦ α), α > 0, x∈R . In each of these approximations, we give a numerical bound on the growth of the function and we estimate the corresponding error term.
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