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An algorithm of infinite sums representations and Tasoev continued fractions


Author: Takao Komatsu
Journal: Math. Comp. 74 (2005), 2081-2094
MSC (2000): Primary 11A55, 11J70, 11Y16
Published electronically: February 14, 2005
MathSciNet review: 2164115
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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.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01752-7
Keywords: Continued fractions, infinite sums, Tasoev continued fractions
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).
Article copyright: © Copyright 2005 American Mathematical Society