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The convergence of padé approximants and their generalizations

  • 4. The Padé Approximation, the Riemann Boundary Value Problem and Arithmetic Applications
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The Riemann Problem, Complete Integrability and Arithmetic Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 925))

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References

  1. E. Hiile, “Analytic Function Theory”, Vol. II. Ginn and Co., Waltham, Mass. (1962) p 275.

    Google Scholar 

  2. J. Nuttall, “On Sets of Minimum Capacity” preprint, 1980.

    Google Scholar 

  3. J. Nuttall, “Sets of Minimum Capacity, Padé Approximants and the Bubble Problem”, Cargese Summer School on Bifurcation Phenomena and Related Topics” (1979).

    Google Scholar 

  4. G. Szego, “Orthogonal Polynomials”, American Mathematical Society, New York, (1959).

    MATH  Google Scholar 

  5. J. Nuttall and S. R. Singh, “Orthogonal Polynomials and Padé Approximants Associated with a System of Arcs”, J. Approx. Theory 21, (1977), 1–42.

    Article  MathSciNet  MATH  Google Scholar 

  6. N. I. Akhiezer, “Orthogonal Polynomials on General Intervals”, Soviet Math. Doklady, 1 (1960), 989–992.

    MATH  Google Scholar 

  7. C. L. Siegel, “Topics in Complex Function Theory”, Interscience, New York, (1971).

    MATH  Google Scholar 

  8. J. Nuttall and C. J. Wherry, “Gaussian Integration for Complex Weight Functions”, J. Inst. Maths Applics 21 (1978), 165–170.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. L. Gammel and J. Nuttall, “Note on Generalized Jacobi Polynomials,” lecture in this volume.

    Google Scholar 

  10. C. Hermite, “Sur la generalisation des fractions continues algebriques”. Jour. de Math., ser. 4, 10 (1894), 291–329.

    Google Scholar 

  11. H. Padé, “Sur la generalisation des fractions continues algebriques”, Annali di Math. ser. 2, 21 (1893), 289–308.

    Google Scholar 

  12. J. Nuttall, “Hermite-Padé Approximants to Meromorphic Functions” preprint, 1980.

    Google Scholar 

  13. R. E. Shafer, “On Quadratic Approximation”, SIAM J. Numer. Anal. 11, (1974), 447–460.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. V. Chudnovsky, “Padé Approximation and the Riemann Monodromy Problem,” Cargese Summer School on Bifurcation Phenomena and Related Topics (1979).

    Google Scholar 

  15. S. K. Burley, S. O. John and J. Nuttall, “Vector Orthogonal Polynomials” preprint, 1980.

    Google Scholar 

  16. R. T. Baumel, J. L. Gammel and J. Nuttall, “Asymptotic Form of Hermite-Padé Polynomials” in preparation.

    Google Scholar 

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David V. Chudnovsky Gregory V. Chudnovsky

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© 1982 Springer-Verlag

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Nuttall, J. (1982). The convergence of padé approximants and their generalizations. In: Chudnovsky, D.V., Chudnovsky, G.V. (eds) The Riemann Problem, Complete Integrability and Arithmetic Applications. Lecture Notes in Mathematics, vol 925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093513

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  • DOI: https://doi.org/10.1007/BFb0093513

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11483-3

  • Online ISBN: 978-3-540-39152-4

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