Nth-root asymptotics of orthonormal polynomials and non-diagonal pade approximants

  • Herbert Stahl
Part of the Lecture Notes in Mathematics book series (LNM, volume 1329)


Connections between n-th root asymptotics of orthonormal polynomials associated with measures of first and second kind are investigated. This problem arises in the study of convergence and divergence of essentially non-diagonal sequences of Padé approximants to Markov functions.


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  1. [ErTu]
    P. Erdös and P. Turan: On Interpolation III; Ann. of Math 41 (1940) pp. 510–553.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [GrM]
    P.R. Graves-Morris: The Convergence of Ray Sequences of Padé Approximants of Stieltjes Functions; J. Comp. and Appl. Math. 7, (1981), pp. 191–201.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [Ma]
    A. Markov: Deux demonstrations de la convergence de certaines fractions continues; Act. Math. 19, (1895), pp. 93–104.MathSciNetCrossRefGoogle Scholar
  4. [Pe]
    O. Perron: Die Lehre von den Kettenbruchen; Chelsea, New York 1929.Google Scholar
  5. [Sa]
    E.B. Saff: Incomplete and Orthogonal Polynomials; in: Approximation Theory IV, Eds.: C.K. Chui et al., Academic Press, New York 1983, pp. 219–255.Google Scholar
  6. [St1]
    H. Stahl: Beiträge zum Problem der Konvergenz von Padéapproximierenden, Dissertation, TU-Berlín 1976.Google Scholar
  7. [St2]
    H. Stahl: Non-Diagonal Padé Approximants to Markov Functions; in: Approximation Theory V, Eds.: C.K. Chui et al., Academic Press, New York 1986, pp. 571–574.Google Scholar
  8. [St3]
    H Stahl: Nth-Root Asymptotics of Orthogonal Polynomials Associated with General Measures; Manuscript, TFH-Berlin, 1987.Google Scholar
  9. [U1]
    J.L. Ullman: A Survey of Exterior Asymptotics for Orthogonal Polynomials Associated with a Finite Interval and a Study of the Case of General Weight Measures; in: Approximation Theory and Spline Functions. Eds.: S.P. Singh et al., D. Reidel, Dodrecht 1984, pp. 467–478.Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Herbert Stahl
    • 1
  1. 1.Technische Fachhochschule Berlin/FB 2Berlin 65Germany

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