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Modification of generalised continued fractions I definition and application to the limit-periodic case

Continued Fractions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1237)

Abstract

The aim of this paper is to generalise the concept of "modification", which has been so successfully exploited in the field of ordinary continued fractions, to generalised continued fractions.

The main result in this paper is the proof of convergence acceleration for a suitable modification in the case of limit-1-periodic n-fractions for which the auxiliary equation (connected with the underlying difference equation for numerators and denominators) has only simple roots with differing absolute values.

Keywords

  • Simple Root
  • Continue Fraction
  • Finite Limit
  • Auxiliary Equation
  • Positive Real Root

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1987 Springer-Verlag

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de Bruin, M.G., Jacobsen, L. (1987). Modification of generalised continued fractions I definition and application to the limit-periodic case. In: Gilewicz, J., Pindor, M., Siemaszko, W. (eds) Rational Approximation and its Applications in Mathematics and Physics. Lecture Notes in Mathematics, vol 1237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072462

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  • DOI: https://doi.org/10.1007/BFb0072462

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17212-3

  • Online ISBN: 978-3-540-47412-8

  • eBook Packages: Springer Book Archive