An error estimate for continued fractions

Author:
John Gill

Journal:
Proc. Amer. Math. Soc. **96** (1986), 71-74

MSC:
Primary 40A15; Secondary 30B70

DOI:
https://doi.org/10.1090/S0002-9939-1986-0813813-1

MathSciNet review:
813813

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Abstract: New and improved truncation error bounds are derived for continued fractions , where . The geometrical approach is somewhat unusual in that it involves both isometric circles and fixed points of bilinear transformations.

**[1]**L. R. Ford,*Automorphic functions*, McGraw-Hill, New York, 1929, pp. 23-30.**[2]**J. Gill,*Converging factors for continued fractions*, Proc. Amer. Math. Soc.**84**(1982), 85-88. MR**633283 (82k:30006)****[3]**-,*Truncation error analysis for continued fractions*,*where*, Lecture Notes in Math., vol. 932, Springer-Verlag, Berlin and New York, 1982, pp. 71-73.**[4]**-,*Modifying factors for sequence of linear fractional transformations*, Norske Vid. Selsk. Skr. (Trondheim)**3**(1978), 1-7.**[5]**W. Jones and R. Snell,*Truncation error bounds for continued fractions*, SIAM J. Numer. Anal.**6**(1969), 210-221. MR**0247737 (40:1000)****[6]**W. Thron and W. Waadeland,*Accelerating convergence of limit periodic continued fractions*, Numer. Math.**34**(1980), 155-170. MR**566679 (81e:30008)****[7]**-,*Truncation error bounds for limit periodic continued fractions*, Math. Comp.**40**(1983), 589-597. MR**689475 (84f:30009)**

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0813813-1

Article copyright:
© Copyright 1986
American Mathematical Society