39
Views
1
CrossRef citations to date
0
Altmetric
Research Article

SEL Egyptian fraction expansion and characterizations of rational numbers

&
Pages 277-298 | Received 01 Jun 2020, Published online: 05 Jan 2021

References

  • A. Beck, M. N. Bleicher and D. W. Crowe, Excursions into Mathematics, Worth Publishers, New York, 1968.
  • R. Cohen, Egyptian fraction expansions, Math. Mag. 46(1973), no. 2, 76-80. doi: 10.1080/0025570X.1973.11976280
  • P. Erdös, The solution in whole number of the equation , Mat. Lapok 1(1950), 192-210 (in Hungarian).
  • P. Erdös, A. Rényi, and P. Szüsz, On Engel’s and Sylvester’s series, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 1(1958), 7-32.
  • P. Erdös and J. O. Shallit, New bounds on the length of finite Pierce and Engel series, J. Théor. Nombres Bordeaux 3(1991), no. 1, 43-53. doi: 10.5802/jtnb.41
  • P. Erdös and S. Stein, Sums of distinct unit fractions, Proc. Amer. Math. Soc.14(1963), no.1, 126-131. doi: 10.1090/S0002-9939-1963-0142502-9
  • J. Galambos, Some remarks on the Lüroth expansion, Czechoslovak Math. J. 22(1972), no. 2, 266-271. doi: 10.21136/CMJ.1972.101097
  • J. Galambos, Representations of Real Numbers by Infinite Series, vol. 502 of Lecture Notes in Mathematics, Springer, New York, 1976.
  • S. W. Golomb, An algebraic algorithm for the representation problems of the Ahmes papyrus, Amer. Math. Monthly 69(1962), no. 8, 785–787.
  • N. R. Kanasri and P. Singthongla, Characterizations of rational numbers by SEL series and alternating SEL series expansions, Songklanakarin J. Sci. Technol. 40(2018), no. 4, 743-751.
  • A. Knopfmacher and J. Knopfmacher, Two concrete new constructions of the real numbers, Rocky Mountain J. Math. 18(1988), no. 4, 813-824. doi: 10.1216/RMJ-1988-18-4-813
  • V. Laohakosol, T. Chaichana, J. Rattanamoong, and N. R. Kanasri, Engel series and Cohen-Egyptian fraction expansions, Int. J. Math. Math. Sci., Article ID 865705 (2009), 15 pages.
  • M. E. Mays, A worst case of the Fibonacci-Sylvester expansion, J. Combin. Math. Combin. Comput. 1(1987), 141-148.
  • O. Perron, Irrationalzahlen, De Gruyter, Berlin, 1939.
  • O. Perron, Irrationalzahlen, Chelsea, New York, 1951.
  • L. Pisano, Scritti, vol. 1, B. Boncompagni, Rome, 1857.
  • A. Rényi, A new approach to the theory of Engel’s series, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 5(1962), 25-32.
  • H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly 54(1947), no. 3, 135-142. doi: 10.1080/00029890.1947.11991798
  • H. E. Salzer, Further remarks on the approximation of numbers as sums of reciprocals, Amer. Math. Monthly 55(1948), no.6, 350-356.
  • P. Singthongla and N. R. Kanasri, SEL series expansion and generalized model construction for the real number system via series of rationals, Int. J. Math. Math. Sci., Article ID 654319, (2014), 8 pages.
  • J. J. Sylvester, On a point in the theory of vulgar fractions, Amer. J. Math. 3(1880), no. 4, 332-335. doi: 10.2307/2369261

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.