Timeline for Two conjectural infinite series for $\pi$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16, 2021 at 10:27 | vote | accept | Pedja | ||
| Sep 16, 2021 at 9:43 | answer | added | Mastrem | timeline score: 10 | |
| Sep 16, 2021 at 9:30 | comment | added | Pedja | @Carl-FredrikNybergBrodda en.wikipedia.org/wiki/… | |
| Sep 16, 2021 at 9:18 | comment | added | Mastrem | Isn't the second series just $3\cdot L(1,\chi)$, where $\chi$ is the non-trivial Dirichlet character modulo $6$? And the product of the two series is $9\cdot \prod_{p\ge 5}(1-p^{-2})^{-1}=6\zeta(2)=\pi^2$? | |
| Sep 16, 2021 at 9:14 | comment | added | Carl-Fredrik Nyberg Brodda | @PeđaTerzić Which formula of Euler's did you have in mind (if a specific one)? | |
| Sep 16, 2021 at 8:59 | comment | added | Sylvain JULIEN | I think Ramanujan produced a formula along these lines, for expressions the product of which equals $\pi^2$. | |
| Sep 16, 2021 at 8:58 | comment | added | Sylvain JULIEN | Perhaps one could take advantage of the fact that the product of the LHS equals $\pi^2$. | |
| Sep 16, 2021 at 8:52 | comment | added | Pedja | @gmvh There is a similar series for $\pi$ in the literature given by Euler. | |
| Sep 16, 2021 at 8:50 | comment | added | gmvh | So is there another reason besides the numerical coincidence to believe this conjecture? | |
| Sep 16, 2021 at 8:49 | comment | added | Pedja | @gmvh Perhaps it converges very slowly. | |
| Sep 16, 2021 at 8:48 | comment | added | Pedja | @FedorPetrov Right. | |
| Sep 16, 2021 at 8:45 | comment | added | gmvh | The first one doesn't seem to be particularly close from the SageMath cell linked. | |
| Sep 16, 2021 at 8:40 | comment | added | Fedor Petrov | you count prime divisors with multiplicity, right? | |
| Sep 16, 2021 at 8:37 | history | asked | Pedja | CC BY-SA 4.0 |