Narakorn Rompurk Kanasri and Patiwat Singthongla

DOI: 10.14456/sjst-psu.2018.97

pp. 743 - 751

Abstract

We establish characterizations of rational numbers by using SEL series expansions, which yield generalized versions of
characterizing rational numbers by Sylvester series, Engel series and Lüroth series expansions. Characterizations of rational
numbers via alternating SEL series expansions yield generalized versions of characterizing rational numbers by alternating
Sylvester series, alternating Engel series and alternating Lüroth series expansions

Keywords

• Sylvester and alternating Sylvester series
• Engel and alternating Engel series
• Lüroth and alternating Lüroth series
• SEL and alternating SEL series