Timeline for $\cos(\frac{x}{3})\cos(\frac{x}{9})\cos(\frac{x}{27})\dots$ as $x \rightarrow \infty$

11 events

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Jul 17, 2022 at 23:12	comment	added	Jorge Zuniga		I doubt this product has a closed form expression for general $a$. The closest expression I know is for $a=3$ $$\prod_{n=1}^\infty \frac{4\cos^2(x/3^k)-1}{3}=\frac{\sin x}{x}$$
Jul 17, 2022 at 21:31	history	edited	Pluviophile	CC BY-SA 4.0	added 2 characters in body
Jul 17, 2022 at 21:30	comment	added	Pluviophile		At the beginning I had in mind the general question but only asked for $a=3$ thinking an answer for this particular case works for all $a>2$. As it turns out the answer is simple but hard to extend to a continuous domain. It seems that the number-theoretic aspect of $a$ plays an essential role here.
Jul 17, 2022 at 20:47	history	edited	Pluviophile	CC BY-SA 4.0	edited title
Jul 17, 2022 at 20:02	history	edited	Pluviophile	CC BY-SA 4.0	added 176 characters in body
Jul 17, 2022 at 19:54	history	edited	Pluviophile	CC BY-SA 4.0	deleted 174 characters in body
Jul 17, 2022 at 19:51	comment	added	Carlo Beenakker		you will want to ask a new question, which can then be answered and accepted; combining two questions into one is not advised.
Jul 17, 2022 at 19:42	history	edited	Pluviophile	CC BY-SA 4.0	added 174 characters in body
Jul 17, 2022 at 19:35	vote	accept	Pluviophile
Jul 17, 2022 at 19:31	answer	added	Noam D. Elkies		timeline score: 9
Jul 17, 2022 at 19:20	history	asked	Pluviophile	CC BY-SA 4.0