Compatibility of Continued Fraction Convergents with Padé Approximants

  • Jacek Gilewicz
  • Radosław Jedynak
Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)


A Padé approximant (PA) to a function f is a rational function P m Q n matching the power expansion of f at least up to the (m + n)th power. On the contrary, the convergents of the Stieltjes, Jacobi, or Thiele continued fractions (CF) of f define all PA of f. However, the convergents of general CF are not necessarily PA. In this work, we present the rules stating when the convergents of CF are consistent with PA. The similar problem of compatible transformations of a variable and a function applied to PA was studied in [1].


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  1. 1.
    Gilewicz, J.: Approximants de Padé. Lecture Notes in Mathematics, vol. 667, Springer, Berlin (1978)Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centre de Physique Théorique, CNRSMarseille Cedex 09France
  2. 2.Politechnika Radomska im. K. PułaskiegoRadomPoland

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