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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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An algorithm of infinite sums representations and Tasoev continued fractions
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by Takao Komatsu PDF
Math. Comp. 74 (2005), 2081-2094 Request permission

Abstract:

For any given real number, its corresponding continued fraction is unique. However, given an arbitrary continued fraction, there has been no general way to identify its corresponding real number. In this paper we shall show a general algorithm from continued fractions to real numbers via infinite sums representations. Using this algorithm, we obtain some new Tasoev continued fractions.
References
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Additional Information
  • Takao Komatsu
  • Affiliation: Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki University, Hirosaki, 036-8561 Japan
  • Email: komatsu@cc.hirosaki-u.ac.jp
  • Received by editor(s): November 5, 2003
  • Received by editor(s) in revised form: June 15, 2004
  • Published electronically: February 14, 2005
  • Additional Notes: This work was supported in part by a grant from the Sumitomo Foundation (No. 030110).
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 2081-2094
  • MSC (2000): Primary 11A55, 11J70, 11Y16
  • DOI: https://doi.org/10.1090/S0025-5718-05-01752-7
  • MathSciNet review: 2164115