Bernstein-szegő Theorem on Algebraic S-contours
نویسندگان
چکیده
Given function f holomorphic at infinity, the n-th diagonal Padé approximant to f , say [n/n]f , is a rational function of type (n,n) that has the highest order of contact with f at infinity. Equivalently, [n/n]f is the n-th convergent of the continued fraction representing f at infinity. BernsteinSzegő theorem provides an explicit non-asymptotic formula for [n/n]f and all n large enough in the case where f is the Cauchy integral of the reciprocal of a polynomial with respect to the arcsine distribution on [−1, 1]. In this note, Bernstein-Szegő theorem is extended to Cauchy integrals on the so-called algebraic S-contours.
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