Yattselev, Maxim L.2015-12-302015-12-302015-02Yattselev, M. L. (2015). Nuttall’s theorem with analytic weights on algebraic S-contours. Journal of Approximation Theory, 190, 73–90. http://doi.org/10.1016/j.jat.2014.10.015https://hdl.handle.net/1805/7871Given a function f holomorphic at infinity, the nth diagonal Padé approximant to f, denoted by [n/n]f, is a rational function of type (n,n) that has the highest order of contact with f at infinity. Nuttall’s theorem provides an asymptotic formula for the error of approximation f−[n/n]f in the case where f is the Cauchy integral of a smooth density with respect to the arcsine distribution on [−1,1]. In this note, Nuttall’s theorem is extended to Cauchy integrals of analytic densities on the so-called algebraic S-contours (in the sense of Nuttall and Stahl).en-USPublisher PolicyPadé approximationOrthogonal polynomialsNon-Hermitian orthogonalityArticle