Characterizations of rational numbers by SEL series and alternating SEL series expansions

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