Irrationality and transcendence of infinite series of rational terms

Lazhar Dhaouadi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 4, Pages 803–810
DOI: 10.7546/nntdm.2024.30.4.803-810
Full paper (PDF, 209 Kb)

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Authors and affiliations

Lazhar Dhaouadi
Carthage University, Preparatory Institute for Engineering Studies of Bizerte
7021 Zarzouna, Tunisia

Abstract

The aim of this paper is to prove two results concerning the irrationality and transcendence of a certain class of infinite series which consist of rational numbers and converge very quickly.

Keywords

• Infinite series
• Irrational number
• Transcendental number

2020 Mathematics Subject Classification

• 11J72
• 11J81

References

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5. Mahler, K. (1976). Lectures on Transcendental Numbers. Series “Lecture Notes in Mathematics”, Vol. 546, Springer.
6. Nishioka, K. (1996). Mahler Functions and Transcendence. Series “Lecture Notes in Mathematics”, Vol. 631, Springer, New York.
7. Nyblom, M. A. (2000). A theorem on transcendence of infinite series. Rocky Mountain Journal of Mathematics, 30(3), 1111–1120.
8. Oppenheim, A. (1954). Criteria for irrationality of certain classes of numbers. The American Mathematical Monthly, 61, 235–241.
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Manuscript history

• Received: 31 May 2024
• Revised: 13 November 2024
• Accepted: 26 November 2024
• Online First: 27 November 2024

Copyright information

Ⓒ 2024 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).