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Publication
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| Title of Article |
On the SEL Egyptian fraction expansion for real numbers |
| Date of Acceptance |
14 June 2022 |
| Journal |
| Title of Journal |
AIMS Mathematics |
| Standard |
SCOPUS |
| Institute of Journal |
AIMS Press |
| ISBN/ISSN |
2473-6988 |
| Volume |
2022 |
| Issue |
7 |
| Month |
มิถุนายน |
| Year of Publication |
2022 |
| Page |
15094-15106 |
| 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. |
| Keyword |
SEL Egyptian fraction expansion, upper bound, transcendental number, bijection |
| Author |
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| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ตีพิมพ์แล้ว |
| Level of Publication |
นานาชาติ |
| citation |
true |
| Part of thesis |
true |
| Attach file |
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| Citation |
0
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Journal Publication
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