Open AccessOn the Irrationality and Transcendence of Rational Powers of e
Author(s) -
Sourangshu Ghosh
Publication year - 2021
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2021/v17i230277
Subject(s) - irrationality , transcendence (philosophy) , mathematical proof , irrational number , mathematics , philosophy , euler's formula , rationality , epistemology , pure mathematics , mathematical analysis , geometry
A number that can’t be expressed as the ratio of two integers is called an irrational number. Euler and Lambert were the first mathematicians to prove the irrationality and transcendence of e. Since then there have been many other proofs of irrationality and transcendence of e and generalizations of that proof to rational powers of e. In this article we review various proofs of irrationality and transcendence of rational powers of e founded by mathematicians over the time.