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Asymptotic distribution of poles and zeros of best rational approximants to x α on [0,1]

E. Saff;  H. Stahl — 1995

Banach Center Publications

Let r n * ∈ ℛ n n be the best rational approximant to f ( x ) = x α , 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of r n * lie on the negative axis ℝ < 0 . 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 e n = f - r n * on [0,1], and survey related convergence results.

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