Abstract
Using Nuttall's compact formula for the [ n, n − 1] Pad'e approximant, the authors show that there is a natural connection between the Padé approximants of a series of Stieltjes and orthogonal polynomials. In particular, we obtain the precise error formulas. The [ n, n − 1] Padé 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, Padé approximants converge to the Stieltjes integral.
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