Irrationality of some Series with Rational Terms

Authors

  • Pairit Kuhapatanakul Department of Mathematics, Faculty of Science Kasetsart University, Bangkok 10900, Thailand
  • Vichian Laohakosol Department of Mathematics, Faculty of Science Kasetsart University, Bangkok 10900, Thailand

Keywords:

irrationality, Cantor series, linear recurrences

Abstract

An irrationality criterion due to Diananda and Oppenheim states that a Cantor series of rational terms is rational except possibly when the rational terms are of certain special shapes. In the first part, this excepted case is analyzed and conclusions are drawn for two specific classes of series. Badea in 1993 established very strong irrationality tests for series of positive rational terms and applied them to settle some previous open problems. Later Brown, Pei and Shiue extended Badea’s applications to those series whose terms satisfy linear recurrence relations. Extensions of these results are derived in the second part. AMS Mathematics Classification: 11J72,11B37

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Published

2001-06-30

How to Cite

Kuhapatanakul, Pairit, and Vichian Laohakosol. 2001. “Irrationality of Some Series With Rational Terms”. Agriculture and Natural Resources 35 (2). Bangkok, Thailand:205-9. https://li01.tci-thaijo.org/index.php/anres/article/view/240306.

Issue

Vol. 35 No. 2 (2001): April-June

Section

Research Article

License

online 2452-316X print 2468-1458/Copyright © 2022. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/),
production and hosting by Kasetsart University of Research and Development Institute on behalf of Kasetsart University.