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arXiv · 0911.1929

Irrationality proofs \`a la Hermite

Li Zhou
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Abstract

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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Li Zhou. 2009-11-10. Irrationality proofs \`a la Hermite. https://doi.org/10.1017/s0025557200003491

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