Timeline for Extending Apéry's proof to Catalan's constant?
Current License: CC BY-SA 4.0
31 events
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| Aug 1, 2023 at 13:12 | comment | added | KStar | @JesúsGuillera Big fan of your WZ-pair work! I didn't realise you had previously found this formula for Catalan's constant. Bravo! Credit where it's due :) | |
| Aug 1, 2023 at 12:01 | comment | added | Jesús Guillera | I discovered and proved that formula for the Catalan constant in 2008, arXiv 1104.0396 (Identity 3). | |
| May 30, 2022 at 15:18 | history | edited | KStar | CC BY-SA 4.0 |
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| Aug 8, 2021 at 11:20 | vote | accept | KStar | ||
| S Aug 8, 2021 at 11:19 | history | bounty ended | KStar | ||
| S Aug 8, 2021 at 11:19 | history | notice removed | KStar | ||
| Aug 7, 2021 at 23:50 | answer | added | rgvalenciaalbornoz | timeline score: 18 | |
| Aug 7, 2021 at 18:54 | comment | added | Steven Clark | I'm not sure it provides any new insight, but I've noticed $\eta(2 n+1)$ and $\beta(2 n)$ can both be represented by difference roots for $n\in\mathbb{N}$ (see math.stackexchange.com/q/4219140). | |
| Aug 7, 2021 at 2:15 | comment | added | Steven Clark | There are a few continued fraction representations of Catalan's constant at functions.wolfram.com/Constants/Catalan/10. | |
| Aug 4, 2021 at 21:30 | comment | added | rgvalenciaalbornoz | Doubt 5 can be obtained using the Poincaré-Perron theorem for linear recurrences with non-constant coefficients. I will try to compile everything with examples. | |
| Aug 4, 2021 at 17:35 | comment | added | KStar | Hi, @rgvalenciaalbornoz doubts 5, 6 and 7 are the major doubts that I also have, but I am also somewhat curious about the other doubts listed that weren't answered. | |
| Aug 4, 2021 at 14:23 | comment | added | rgvalenciaalbornoz | Hi, I saw the linked post in MathStackExchange, what are the doubts from the sections that you also have? | |
| S Aug 4, 2021 at 1:44 | history | bounty started | KStar | ||
| S Aug 4, 2021 at 1:44 | history | notice added | KStar | Draw attention | |
| Aug 4, 2021 at 1:31 | history | edited | KStar |
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| Jul 20, 2021 at 7:58 | history | edited | YCor | CC BY-SA 4.0 |
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| Jul 19, 2021 at 18:56 | comment | added | KStar | What piece am I not considering, or what result needs to be first shown, in order for an Apéry-like proof of the irrationality of $G$? | |
| Jul 19, 2021 at 17:32 | history | edited | KStar | CC BY-SA 4.0 |
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| Jul 19, 2021 at 14:57 | history | edited | KStar | CC BY-SA 4.0 |
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| Jul 18, 2021 at 17:35 | comment | added | KStar | A lot of my questions are similar to this post If anyone perhaps knows any other answers to that post. | |
| Jul 18, 2021 at 13:10 | comment | added | Gerry Myerson | @Tim, yes, I know that. It doesn't contradict my statement that there's no proof for $\zeta(5)$. | |
| Jul 18, 2021 at 13:07 | comment | added | Timothy Chow | @GerryMyerson Work of Rivoal and/or Zudilin (e.g., A note on odd zeta values) has shown that certain sets of odd zeta values must contain at least one irrational value. | |
| Jul 18, 2021 at 11:15 | history | edited | KStar | CC BY-SA 4.0 |
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| Jul 18, 2021 at 10:43 | history | edited | KStar | CC BY-SA 4.0 |
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| Jul 18, 2021 at 9:16 | comment | added | KStar | @GerryMyerson I have indeed read that paper; it is quite interesting, but I do not understand where the recursive formulae mentioned in that paper arise from. | |
| Jul 18, 2021 at 3:49 | comment | added | Gerry Myerson | When Apéry's result was announced, a lot of effort went into trying to make his methods work for higher zeta values. To the best of my knowledge, nothing ever panned out (in the sense that no one ever found a way to use Apéry-like methods to prove irrationality for, say, $\zeta(5)$). By the way, I trust you've read Alf van der Poorten's paper on "a proof that Euler missed"? | |
| Jul 17, 2021 at 21:33 | comment | added | Somos | Maybe the answer is at David Bailey, Jonathan Borwein, David Bradley, Experimental determination of Apéry-like identities for zeta(2n+2), arXiv:math/0505270 [math.NT], 2005. | |
| Jul 17, 2021 at 21:18 | comment | added | KStar | @MarkSapir Hmm not quite; it's related and a useful continued fraction to know, but I'm particularly curious in the continued fraction Apéry derived and used to prove $\zeta (3)$ as irrational. | |
| Jul 17, 2021 at 21:15 | comment | added | markvs | Does it answer your question mathoverflow.net/questions/84108/… ? | |
| Jul 17, 2021 at 20:53 | review | Close votes | |||
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| Jul 17, 2021 at 20:24 | history | asked | KStar | CC BY-SA 4.0 |