Mathematics – Classical Analysis and ODEs
Scientific paper
2011-04-27
Mathematics
Classical Analysis and ODEs
Scientific paper
It is not known whether the Flint Hills series $\sum_{n=1}^{\infty} \frac{1}{n^3\cdot\sin(n)^2}$ converges. We show that this question is closely related to the irrationality measure of $\pi$, denoted $\mu(\pi)$. In particular, convergence of the Flint Hills series would imply $\mu(\pi) \leq 2.5$ which is much stronger than the best currently known upper bound $\mu(\pi)\leq 7.6063...$. This result easily generalizes to series of the form $\sum_{n=1}^{\infty} \frac{1}{n^u\cdot |\sin(n)|^v}$ where $u,v>0$. We use the currently known bound for $\mu(\pi)$ to derive conditions on $u$ and $v$ that guarantee convergence of such series.
No associations
LandOfFree
On convergence of the Flint Hills series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On convergence of the Flint Hills series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On convergence of the Flint Hills series will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-475384