On the Irrationality and Transcendence of Rational Powers of e
Sourangshu Ghosh *
Department of Civil Engineering, Indian Institute of Technology Kharagpur, India.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Irrationality, transcendence, Euler’s number