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Let be the best rational approximant to , 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of lie on the negative axis . In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function on [0,1], and survey related convergence results.
Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.
We give the asymptotic formula for the error in linear interpolation with arbitrary knots.
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