Timeline for Numerology with Ramanujan's pi formula
Current License: CC BY-SA 3.0
20 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Aug 19, 2019 at 1:57 | vote | accept | Tito Piezas III | ||
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Apr 4, 2017 at 14:49 | comment | added | Tito Piezas III | @Wolfgang: That is also how H. H. Chan and S. Cooper use it in their "Rational analogues of Ramanujan's series for 1/π". :) | |
| Apr 4, 2017 at 13:52 | comment | added | Wolfgang | Thank you, that helps. So you use it in fact the same way as Michael Somos in his collection of eta identities. Didn't occur to me earlier... | |
| Apr 4, 2017 at 13:25 | comment | added | Tito Piezas III | @Wolfgang: I've added a note regarding the "level". Sorry for the delay. | |
| Apr 4, 2017 at 13:24 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Cooper. And note
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| Apr 4, 2017 at 13:04 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Chan and Zudilin
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| Mar 28, 2017 at 19:25 | comment | added | Wolfgang | Very nice stuff! May you just specify in which sense you use the word «level» here? | |
| Mar 28, 2017 at 3:37 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Added levels
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| Mar 27, 2017 at 15:51 | comment | added | Tito Piezas III | @VladimirDotsenko: I've asked it in another question to format it properly. Kindly see this post. | |
| Mar 27, 2017 at 14:37 | comment | added | Vladimir Dotsenko | @TitoPiezasIII give me some context and I can try. My contact details are on my homepage (link in the profile). | |
| Mar 27, 2017 at 11:09 | comment | added | Tito Piezas III | @VladimirDotsenko: I have an infinite sequence of integers related to this post and perhaps to $\zeta(5)$. Would you be able to find its recurrence if you have enough terms of the sequence? | |
| Mar 26, 2017 at 15:06 | comment | added | Vladimir Dotsenko | FWIW, if we denote by $s_k(\alpha)$ the sum $\sum_{j=0}^k\alpha^{k-2j}\binom{k}{2j}\binom{2j}{j}\binom{2j}{j}$ in your formula, the Wilf-Zeilberger methods seem to produce a recurrence $\alpha(\alpha^2-16)(k+1)(k+2)s_k(\alpha)-(3\alpha^2-16)(k+2)^2s_{k+1}(\alpha)+\alpha(3k^2+15k+19)s_{k+2}(\alpha)-(k+3)^2s_{k+3}(\alpha)=0$ | |
| Mar 26, 2017 at 13:54 | comment | added | Tito Piezas III | @SylvainJULIEN: For any non-zero real number $\alpha$, positive or negative, as long as the denominator does not vanish, or the denominator becomes so small that the series no longer converges | |
| Mar 26, 2017 at 13:48 | comment | added | Sylvain JULIEN | By the way, when you say 'for general $ \alpha $ ', is $ \alpha $ supposed to be an integer or any non negative real number ? Cause if it has to be an integer, maybe one should check $ 1 $-periodicity and all the Fourier related stuff. | |
| Mar 26, 2017 at 13:42 | comment | added | Tito Piezas III | @SylvainJULIEN: I wouldn't know where to start. It was luck and persistence that I detected a pattern. | |
| Mar 26, 2017 at 13:32 | comment | added | Sylvain JULIEN | This is a very naive comment, but have you tried to derive the RHS with respect to $ \alpha $? | |
| Mar 26, 2017 at 13:19 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Improvements
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| Mar 26, 2017 at 3:15 | history | answered | Tito Piezas III | CC BY-SA 3.0 |