The transcendence of e via formal power series
Abstract
We review Hilbert's classical analytical proof of the transcendence of the number e. Then, we show how this result can be obtained algebraically by means of formal power series (FPS). We give two proofs of the transcendence of e based on FPS. The first of them is a specialization of the 1990 proof by Beukers, Bézivin and Robba of the Lindemann-Weierstrass theorem. The second proof is due to this author and is an adaptation of Hilbert's argument to FPS.
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