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Plenary Papers A Priori Truncation Error Bounds for Continued Fractions
- Source :
- Rocky Mountain J. Math. 33, no. 2 (2003), 409-474
- Publication Year :
- 2003
- Publisher :
- Rocky Mountain Mathematics Consortium, 2003.
-
Abstract
- Most of the known continued fraction expansions of special functions are limit periodic. This means that the classical approximants S n (0) are normally not the best ones to use for approximations. In this paper we suggest a number of approximants S n (w n ) which converge faster. The estimation of the improvement and bounds for the error |f - Sn(wn)| (which we still call the truncation error) are mainly obtained by means of Thron's parabola sequence theorem and the oval sequence theorem.
- Subjects :
- Sequence
40A15
convergence
Truncation error (numerical integration)
General Mathematics
Mathematical analysis
complementary error function
incomplete gamma function
30B10
Upper and lower bounds
Limit periodic continued fractions
Combinatorics
Error function
truncation error estimates
Fraction (mathematics)
Limit (mathematics)
Incomplete gamma function
Gamma function
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Rocky Mountain J. Math. 33, no. 2 (2003), 409-474
- Accession number :
- edsair.doi.dedup.....f9bd8e9d179c58ada3db91dc2ec65c76