Irrationality proofs à la Hermite

Details Irrationality proofs à la Hermite Irrationality proofs à la Hermite

2009-11-10

arxiv.org/abs/0911.1929v2

Mathematics

Number Theory

8 pages

Scientific paper

As rewards of reading two great papers of Hermite from 1873, we trace the historical origin of the integral Niven used in his well-known proof of the irrationality of $\pi$, uncover a rarely acknowledged simple proof by Hermite of the irrationality of $\pi^2$, give a new proof of the irrationality of $r\tan r$ for nonzero rational $r^2$, and generalize it to a proof of the irrationality of certain ratios of Bessel functions.

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