PADE APPROXIMATION OF STIELTJES SERIES
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Using Nuttall's compact formula for the [n, n - 1] Pad'e approximant, the authors show that there is a natural connection between the Pad approximants of a series of Stieltjes and orthogonal polynomials. In particular, we obtain the precise error formulas. The [n, n - 1] Pad approximant in this case is just a Gaussian quadrature of the Stieltjes integral. Hence, analysis of the error is now possible and under very mild conditions it is shown that the [n, n + j], j - 1, Pad approximants converge to the Stieltjes integral. 1975.