Timeline for On 12 cfracs: for Catalan's $K$, Gieseking's $\kappa$, and $\pi^2$, $\pi^3$, plus three for $\zeta(3)$ using Zagier's "six sporadic sequences"
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| May 23, 2023 at 5:47 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Made cfrac notation consistent with literature, and added update.
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| May 21, 2023 at 12:10 | answer | added | Ofir Gorodetsky | timeline score: 3 | |
| May 21, 2023 at 4:49 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Re-defined the general cfrac to use ALL the coefficients of the recurrence relation.
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| May 20, 2023 at 12:55 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Made cfracs in this post consistent with cfracs in the next post
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| May 20, 2023 at 11:55 | comment | added | Tito Piezas III | @CHUAKS Not always. In the list, there are 3 cfracs for $\zeta(3)$. The original one by Apery is positive. | |
| May 20, 2023 at 11:46 | comment | added | CHUAKS | Is there any reason or general pattern for the sign of the continued fraction ? For example it seems to be always + for $\zeta(even)$ and - for $\zeta(odd)$ ? | |
| May 20, 2023 at 6:48 | comment | added | Tito Piezas III | Gieseking's constant $\kappa$ seems not so well-known compared to its cousin Catalan's constant $K$. But both are also volumes, the former for the hyperbolic Gieseking 3-manifold, while the latter is 1/4 for the hyperbolic octahedron. Fortunately, I made a large list of contexts for $\kappa$ and $K$ back in 2019 which is why I suspected both might appear in the deg-$2$ continued fractions. Kindly see this MSE post. | |
| May 20, 2023 at 6:25 | vote | accept | Tito Piezas III | ||
| May 20, 2023 at 6:25 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Added Cohen's answer to complete the list.
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| May 19, 2023 at 16:34 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Revamped sections
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| May 19, 2023 at 16:01 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Values of d.
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| May 19, 2023 at 15:21 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
added 86 characters in body
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| May 19, 2023 at 15:08 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Corrected a small typo, and changed some details
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| May 19, 2023 at 14:41 | answer | added | Henri Cohen | timeline score: 13 | |
| May 19, 2023 at 13:23 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Added Gieseking's constant.
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| May 19, 2023 at 12:19 | history | edited | Tito Piezas III | CC BY-SA 4.0 |
Added one closed-form
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| May 19, 2023 at 8:54 | history | asked | Tito Piezas III | CC BY-SA 4.0 |