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arXiv · 0911.1933

Recurrent proofs of the irrationality of certain trigonometric values

Li Zhou·Lubomir Markov
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Abstract

We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary transcendental functions are also discussed.

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Li Zhou, Lubomir Markov. 2009-11-10. Recurrent proofs of the irrationality of certain trigonometric values. https://doi.org/10.4169/000298910x480838

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