Extended numerical computations on the “1/9” conjecture in rational approximation theory

  • A. J. Carpenter
  • A. Ruttan
  • R. S. Varga
Numerical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)


The behavior of the constants λn,n(ex), denoting the errors of best uniform approximation to ez on the interval [0,+∞) by real rational functions having numerator and denominator polynomials of degree at most n, has generated much recent interest in the approximation theory literature. Based on high-precision calculations, we present here the table of constants {λn,n (ex)} n 30 =0, rounded to forty significant digits, and we discuss their significance to related conjectures in this area.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • A. J. Carpenter
    • 1
  • A. Ruttan
    • 1
  • R. S. Varga
    • 1
  1. 1.Institute for Computational MathematiesKent State UniversityKentUSA

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