The irrationality measure of $\pi$ as seen through the eyes of $\cos (n)$

Sully F. Chen, Erin P. J. Pearse

For different values of $\gamma \ge 0$, analysis of the end behavior of the sequence $a_n=\cos (n{)}^{n^{\gamma }}$ yields a strong connection to the irrationality measure of $\pi$. We show that…