Irrationality of some Series with Rational Terms

บทคัดย่อ

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