Rocky Mountain Journal of Mathematics

Padé-type approximants for functions of Markov-Stieltjes type

Lennart Karlberg and Hans Wallin

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Rocky Mountain J. Math., Volume 21, Number 1 (1991), 437-449.

First available in Project Euclid: 5 June 2007

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Karlberg, Lennart; Wallin, Hans. Padé-type approximants for functions of Markov-Stieltjes type. Rocky Mountain J. Math. 21 (1991), no. 1, 437--449. doi:10.1216/rmjm/1181073016.

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  • N.I. Achieser, Vorlesungen über Approximationstheorie, 2 -1967.
  • T. Bagby, On interpolation by rational functions, Duke Math. J. 36 (1969), 95-104.
  • C. Brezinski, Padé-type approximants and general orthogonal polynomials, Birkhauser Verlag, Basel, 1980.
  • W. Gautschi, A survey of Gauss-Christoffel quadrature formulae, in E.B. Christoffel (P.L. Butzer and F. Fehér, Eds.), Birkhäuser Verlag, 1981, 72-147.
  • L. Karlberg, Some convergence results for Padé-type approximants, Dept. of Math., Univ. of Umeå, 11 (1986).
  • J. Karlsson and B. von Sydow, The convergence of Padé approximants to series of Stieltjes, Ark. Mat. 14 (1976), 43-53.
  • D.S. Lubinsky, A survey of general orthogonal polynomials for weights on finite and infinite intervals, Acta Appl. Math. 10 (1987), 237-296.
  • A. Markov, Deux demonstrations de la convergence de certain fractions continues, Acta Math. 19 (1895), 93-104.
  • E.B. Saff, Polynomial and rational approximation in the complex domain, Proc. Sympos. Appl. Math. 36 (1986), 21-49.
  • B. von Sydow, Error estimates for Gaussian quadrature formulae, Numer. Math. 29 (1977), 59-64.
  • W.J. Thron, Quadrature formulae and moment problems, in Proc. Conf. Rational Approximation and Interpolation, Tampa, Florida, Lecture Notes in Math. 1105, Springer-Verlag, Berlin, 1984, 477-488.
  • H. Wallin, Potential Theory and approximation of analytic functions by rational interpolation, in Proc. Coll. Complex Anal. Joensuu, Finland, Lecture Notes in Math. 747, Springer-Verlag, Berlin, 1979, 434-450.
  • --------, Rational interpolation to meromorphic functions, in Proc. Conf. Padé Approximation and its Applications, Amsterdam, Lecture Notes in Math. 888, Springer-Verlag, Berlin, 1981, 371-383.
  • J.L. Walsh, Interpolation and approximation by rational functions in the complex domain, 4th ed., Amer. Math. Soc., Colloq. Publ. XX, Providence, RI, 1965.