@article{Janthawee2022, 
author = {Mayurachat Janthawee and Narakorn R. Kanasri},
title = {On the SEL Egyptian fraction expansion for real numbers},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {15094-15106},
keywords = {SEL Egyptian fraction expansion, upper bound, transcendental number, bijection},
url = {https://www.sciopen.com/article/10.3934/math.2022827},
doi = {10.3934/math.2022827},
abstract = {In the authors' earlier work, the SEL Egyptian fraction expansion for any real number was constructed and characterizations of rational numbers by using such expansion were established. These results yield a generalized version of the results for the Fibonacci-Sylvester and the Engel series expansions. Under a certain condition, one of such characterizations also states that the SEL Egyptian fraction expansion is finite if and only if it represents a rational number. In this paper, we obtain an upper bound for the length of the SEL Egyptian fraction expansion for rational numbers, and the exact length of this expansion for a certain class of rational numbers is verified. Using such expansion, not only is a large class of transcendental numbers constructed, but also an explicit bijection between the set of positive real numbers and the set of sequences of nonnegative integers is established.}
}