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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