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Convergence acceleration for continued fractions K(an/1), where an → ∞

Continued Fractions

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

Abstract

We introduce a method of convergence acceleration for a class of continued fractions K(an/1) where an → ∞. By using the modifying factors \({w_n} = \sqrt {{a_{n + 1}} + 1/4} - 1/2\), we obtain an improvement roughly like |f-Sn(wn)|/|f-Sn(0)|≤c|an+1|-1.

Keywords

  • Limit Point
  • Hypergeometric Function
  • Continue Fraction
  • Convergence Region
  • Continue Fraction Expansion

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References

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© 1987 Springer-Verlag

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Jacobsen, L., Jones, W.B., Waadeland, H. (1987). Convergence acceleration for continued fractions K(an/1), where an → ∞. 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/BFb0072463

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  • DOI: https://doi.org/10.1007/BFb0072463

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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