Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An algorithm of infinite sums representations and Tasoev continued fractions
HTML articles powered by AMS MathViewer

by Takao Komatsu PDF
Math. Comp. 74 (2005), 2081-2094 Request permission


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.
  • William B. Jones and Wolfgang J. Thron, Continued fractions, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley Publishing Co., Reading, Mass., 1980. Analytic theory and applications; With a foreword by Felix E. Browder; With an introduction by Peter Henrici. MR 595864
  • Takao Komatsu, On Tasoev’s continued fractions, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 1, 1–12. MR 1937787, DOI 10.1017/S0305004102006266
  • Takao Komatsu, On Hurwitzian and Tasoev’s continued fractions, Acta Arith. 107 (2003), no. 2, 161–177. MR 1970821, DOI 10.4064/aa107-2-4
  • Takao Komatsu, Simple continued fraction expansions of some values of certain hypergeometric functions, Tsukuba J. Math. 27 (2003), no. 1, 161–173. MR 1999242, DOI 10.21099/tkbjm/1496164567
  • L. A. Lyusternik, O. A. Chervonenkis, and A. R. Yanpol′skii, Handbook for computing elementary functions, Pergamon Press, Oxford-Edinburgh-New York, 1965. Translated from the Russian by G. J. Tee; Translation edited by K. L. Stewart. MR 0183102
  • Christopher G. Pinner, More on inhomogeneous Diophantine approximation, J. Théor. Nombres Bordeaux 13 (2001), no. 2, 539–557 (English, with English and French summaries). MR 1879672
  • A. J. van der Poorten, Continued fraction expansions of values of the exponential function and related fun with continued fractions, Nieuw Arch. Wisk. (4) 14 (1996), no. 2, 221–230. MR 1402843
  • B. G. Tasoev, Certain problems in the theory of continued fractions, Trudy Tbiliss. Univ. Mat. Mekh. Astronom. 16-17 (1984), 53–83 (Russian, with Georgian summary). MR 853713
  • B. G. Tasoev, On rational approximations of some numbers, Mat. Zametki 67 (2000), no. 6, 931–937 (Russian, with Russian summary); English transl., Math. Notes 67 (2000), no. 5-6, 786–791. MR 1820647, DOI 10.1007/BF02675633
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 11A55, 11J70, 11Y16
  • Retrieve articles in all journals with MSC (2000): 11A55, 11J70, 11Y16
Additional Information
  • Takao Komatsu
  • Affiliation: Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki University, Hirosaki, 036-8561 Japan
  • Email:
  • 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:
  • MathSciNet review: 2164115