Timeline for Possible new series for $\pi$
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 22 at 1:09 | answer | added | Jorge Zuniga | timeline score: 2 | |
| Jul 20 at 6:01 | answer | added | Dan Romik | timeline score: 6 | |
| Jul 19 at 23:24 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added links
|
| Jul 5 at 17:26 | comment | added | Jorge Zuniga | @Timothy_Chow, with $-s_1=\nu$ and $-s_2=1-\nu$ and $\nu\in\mathbb{Q}$ an infinite bi-parametric series for $\pi$ with the algebraic factor $\sin(\nu\pi)$ is got. $\nu=1/6$ gives another rational series. Since this is a sui generis Beta function expansion, a lemniscate constant series with $s_1=s_2=-1/4$ is got, as well as expressions for other trascendental constants like $\Gamma(1/3)$ with $s_1=s_2=-1/3$. The paper also brings a 2nd Beta function expansion with a different rational argument for Pochhamers. One can apply the same approach as above to get other infinite families of series | |
| Jul 5 at 12:07 | comment | added | Timothy Chow | @ModsAndStaffAreNotFair That "Mind Your Decisions" video is a pretty accurate layman's summary of the formula, but it doesn't help answer the question. | |
| Jul 5 at 7:22 | comment | added | Martin.s | youtu.be/t1ZnptSEPI8?si=upACg5uF97FQQ5Gc | |
| Jul 2 at 13:05 | answer | added | Hjalmar Rosengren | timeline score: 18 | |
| Jun 29 at 9:43 | comment | added | Kasper Andersen | @PeterTaylor I think one needs $\Re(\lambda)>-1$ for the series to converge. | |
| Jun 28 at 19:31 | answer | added | Fred Hucht | timeline score: 6 | |
| Jun 28 at 18:10 | history | notice removed | Asaf Karagila♦ | ||
| Jun 28 at 17:49 | comment | added | Nemo | For a series that contains Pochhammer symbol of rational function of $n$ see Theorem 7.1 in this article link.springer.com/article/10.1023/A:1009809424076 | |
| Jun 28 at 15:40 | vote | accept | Timothy Chow | ||
| Jun 28 at 6:52 | history | notice added | TheSimpliFire | Authoritative reference needed | |
| Jun 27 at 14:47 | history | protected | Stefan Kohl♦ | ||
| Jun 27 at 13:34 | history | edited | Peter Taylor |
Add tag reference-request, since the main question is whether it's new
|
|
| Jun 26 at 22:02 | answer | added | Henri Cohen | timeline score: 21 | |
| Jun 26 at 18:03 | review | Suggested edits | |||
| Jun 27 at 2:54 | |||||
| Jun 26 at 11:04 | answer | added | TheSimpliFire | timeline score: 22 | |
| Jun 26 at 10:40 | comment | added | Peter Taylor | Not quite an arbitrary complex number: it needs to avoid the poles at negative integers. Also worth noting (as they do in the paper) that the $\lambda \to \infty$ limit gives the Leibniz formula, which may be useful in literature searches. | |
| Jun 26 at 9:31 | answer | added | Gerry Myerson | timeline score: 23 | |
| Jun 26 at 5:15 | answer | added | Jesús Guillera | timeline score: 31 | |
| Jun 26 at 2:16 | comment | added | Steven Stadnicki | You might also want to keep an eye on math.stackexchange.com/questions/4937730/… (which at least as of yet has no answers) ; I didn't ask it there but I'm also curious as to whether this formula is fundamentally new; I'll be keeping an eye on this too. | |
| Jun 26 at 1:52 | history | asked | Timothy Chow | CC BY-SA 4.0 |