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Location of poles of Padé approximants to entire functions

  • J. Nuttall
Location Of Zeros And Poles
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

We give a conjecture for a set of arcs approached asymptotically by the poles of Padé approximants to entire functions. In two examples the conjecture is shown to be correct and in a third numerical evidence supporting its validity is given.

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References

  1. 1.
    Baumel, R.T., J.L. Gammel, and J. Nuttall, Asymptotic form of Hermite-Padé polynomials, IMA J.Appl.Math.27 (1981), 335–357.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Edrei, A., E.B. Saff, and R.S. Varga, Zeros of sections of power series, Lect. Notes in Math. 1002 (1983).Google Scholar
  3. 3.
    Gončar, A.A., and E.A. Rahmanov, On the convergence of simultaneous Padé approximants for systems of functions of Markov type, Proc. Steklov Math. Inst. 157 (1981), 31–48.Google Scholar
  4. 4.
    Muskhelishvili, N.I., Singular Integral Equations, Noordhoff, Groningen, 1953.zbMATHGoogle Scholar
  5. 5.
    Nuttall, J., The convergence of Padé approximants to functions with branch points, Padé and Rational Approximation (E.B. Saff and R.S. Varga, eds.) pp 101–109. Academic Press, New York, 1977.CrossRefGoogle Scholar
  6. 6.
    Nuttall, J., Sets of minimum capacity, Padé approximants and the bubble problem, Bifurcation Phenomena in Mathematical Physics and Related Topics (C. Bardos and D. Bessis, eds.) pp 185–201. D. Reidel, Dordrecht, 1980.CrossRefGoogle Scholar
  7. 7.
    Nuttall, J., Asymptotics of diagonal Hermite-Padé polynomials, J. Approx. Theory, to appear.Google Scholar
  8. 8.
    Nuttall, J., and S.R. Singh, Orthogonal polynomials and Padé approximants associated with a system of arcs, J. Approx. Theory 21 (1977), 1–42.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Saff, E.B., Incomplete and orthogonal polynomials, Proceedings of Approximation Theory Conference, Texas A & M University, 1983, to appear.Google Scholar
  10. 10.
    Staff, E.B., and R.S. Varga, eds., Padé and Rational Approximation, Academic Press, New York, 1977.Google Scholar
  11. 11.
    Staff, E.B., and R.S. Varga, On the zeros and poles of Padé approximants to ez II, Padé and Rational Approximation (E.B. Saff and R.S. Varga, eds.), pp 195–213. Academic Press, New York, 1977.Google Scholar
  12. 12.
    Saff, E.B., and R.S. Varga, On the zeros and poles of Padé approximants to ez III, Numer. Math. 30 (1978), 241–266.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Stahl, H., Beiträge zum Problem der Konvergenz von Padéapproximierenden, Dissertation, Technischen Universität Berlin (1976).Google Scholar
  14. 14.
    Szegö, G., Orthogonal Polynomials, American Mathematical Society, Providence, 1978.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. Nuttall
    • 1
  1. 1.Department of PhysicsUniversity of Western OntarioLondonCanada

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