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On Transcendental Numbers: New Results and a Little History
Version 1
: Received: 16 January 2018 / Approved: 19 January 2018 / Online: 19 January 2018 (04:07:39 CET)
How to cite: Marcus, S.; Nichita, F.F. On Transcendental Numbers: New Results and a Little History. Preprints 2018, 2018010178 (doi: 10.20944/preprints201801.0178.v1). Marcus, S.; Nichita, F.F. On Transcendental Numbers: New Results and a Little History. Preprints 2018, 2018010178 (doi: 10.20944/preprints201801.0178.v1).
Abstract
Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π, and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication.
Subject Areas
Euler's relation; transcendental numbers; transcendental operations / functions; transcendence; Yang-Baxter equation; hyperbolic functions, logical implication
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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